1. CJM Online first
 Bernardi, Olivier; Curien, Nicolas; Miermont, Grégory

A Boltzmann approach to percolation on random triangulations
We study the percolation model on Boltzmann triangulations using
a generating function approach. More precisely, we consider a
Boltzmann model on the set of finite planar triangulations, together
with a percolation configuration (either sitepercolation or
bondpercolation) on this triangulation.
By enumerating triangulations with boundaries according to both
the boundary length and the number of vertices/edges on the boundary,
we are able to identify a phase transition for the geometry of
the origin cluster.
For instance, we show that the probability that a percolation
interface has length $n$ decays exponentially with $n$ except
at a particular value $p_c$ of the percolation parameter $p$
for which the decay is polynomial (of order $n^{10/3}$). Moreover,
the probability that the origin cluster has size $n$ decays
exponentially if $p\lt p_c$ and polynomially if $p\geq p_c$.
The critical percolation value is $p_c=1/2$ for site percolation,
and $p_c=\frac{2\sqrt{3}1}{11}$ for bond percolation. These
values coincide with critical percolation thresholds for infinite
triangulations identified by Angel for sitepercolation, and
by Angel and Curien for bondpercolation, and we give an independent
derivation of these percolation thresholds.
Lastly, we revisit the criticality conditions for random Boltzmann
maps, and argue that at $p_c$, the percolation clusters conditioned
to have size $n$ should converge toward the stable map of parameter
$ \frac{7}{6}$ introduced by Le Gall and Miermont. This enables
us to derive heuristically some new critical exponents.
Keywords:random map, stable map, critical percolation, gasket Categories:60K35, 60D05, 05A16 

2. CJM 2018 (vol 70 pp. 1096)
 Müllner, Clemens

The RudinShapiro Sequence and Similar Sequences are Normal Along Squares
We prove that digital sequences modulo $m$ along squares are
normal,
which covers some prominent sequences like the sum of digits
in base $q$ modulo $m$, the RudinShapiro sequence and some generalizations.
This gives, for any base, a class of explicit normal numbers
that can be efficiently generated.
Keywords:RudinShapiro sequence, digital sequence, normality, exponential sum Categories:11A63, 11B85, 11L03, 11N60, 60F05 

3. CJM Online first
 Mingo, James A.; Popa, Mihai

Freeness and The Partial Transposes of Wishart Random Matrices
We show that the partial transposes of complex Wishart
random matrices are asymptotically free. We also investigate
regimes where the number of blocks is fixed but the size of
the blocks increases. This gives a example where the partial
transpose produces freeness at the operator level. Finally
we investigate the case of real Wishart matrices.
Keywords:free probability, random matrix, partial transpose, quantum information theory Categories:15B52, 46L54, 60B20 

4. CJM Online first
5. CJM 2017 (vol 70 pp. 3)
 BenaychGeorges, Florent; Cébron, Guillaume; Rochet, Jean

Fluctuation of matrix entries and application to outliers of elliptic matrices
For any family of $N\times N$ random matrices $(\mathbf{A}_k)_{k\in
K}$ which is invariant, in law, under unitary conjugation, we
give general sufficient conditions for central limit theorems
for random variables of the type $\operatorname{Tr}(\mathbf{A}_k
\mathbf{M})$, where the matrix $\mathbf{M}$ is deterministic
(such random variables include for example the normalized matrix
entries of the $\mathbf{A}_k$'s). A consequence is the asymptotic
independence of the projection of the matrices $\mathbf{A}_k$
onto the subspace of null trace matrices from their projections
onto the orthogonal of this subspace. These results are used
to study the asymptotic behavior of the outliers of a spiked
elliptic random matrix. More precisely, we show that the fluctuations
of these outliers around their limits can have various rates
of convergence, depending on the Jordan Canonical Form of the
additive perturbation. Also, some correlations can arise between
outliers at a macroscopic distance from each other. These phenomena
have already been observed
with random matrices
from the Single Ring Theorem.
Keywords:random matrix, Gaussian fluctuation, spiked model, elliptic random matrix, Weingarten calculus, Haar measure Categories:60B20, 15B52, 60F05, 46L54 

6. CJM Online first
 Handelman, David

Nearly approximate transitivity (AT) for circulant matrices
By previous work of Giordano and the author, ergodic
actions of $\mathbf Z$ (and other discrete groups) are completely classified
measuretheoretically by their dimension space, a construction
analogous to the dimension group used in C*algebras and topological
dynamics. Here we investigate how far from AT (approximately
transitive) can actions be which derive from circulant (and related)
matrices. It turns out not very: although nonAT actions can
arise from this method of construction, under very modest additional
conditions, ATness arises; in addition, if we drop the positivity
requirement in the isomorphism of dimension spaces, then all
these ergodic actions satisfy an analogue of AT. Many examples
are provided.
Keywords:approximately transitive, ergodic transformation, circulant matrix, hemicirculant matrix, dimension space, matrixvalued random walk Categories:37A05, 06F25, 28D05, 46B40, 60G50 

7. CJM 2017 (vol 69 pp. 481)
 CorderoErausquin, Dario

Transport Inequalities for Logconcave Measures, Quantitative Forms and Applications
We review some simple techniques based on monotone mass transport
that allow us to obtain transporttype inequalities for any
logconcave
probability measure, and for more general measures as well. We
discuss quantitative forms of these inequalities, with application
to the BrascampLieb variance inequality.
Keywords:logconcave measures, transport inequality, BrascampLieb inequality, quantitative inequalities Categories:52A40, 60E15, 49Q20 

8. CJM 2015 (vol 68 pp. 129)
 Shiozawa, Yuichi

Lower Escape Rate of Symmetric Jumpdiffusion Processes
We establish an integral test on the lower escape rate
of symmetric jumpdiffusion processes generated by regular Dirichlet
forms.
Using this test, we can find the speed of particles escaping
to infinity.
We apply this test to symmetric jump processes of variable order. We also derive the upper and lower escape rates of time changed
processes
by using those of underlying processes.
Keywords:lower escape rate, Dirichlet form, Markov process, time change Categories:60G17, 31C25, 60J25 

9. CJM 2014 (vol 66 pp. 1358)
 Osėkowski, Adam

Sharp Localized Inequalities for Fourier Multipliers
In the paper we study sharp localized $L^q\colon L^p$ estimates for
Fourier multipliers resulting from modulation of the jumps of
LÃ©vy
processes.
The proofs of these estimates rest on probabilistic methods and
exploit related sharp bounds for differentially subordinated
martingales, which are of independent interest. The lower bounds
for
the constants involve the analysis of laminates, a family of
certain
special probability measures on $2\times 2$ matrices. As an
application, we obtain new sharp bounds for the real and imaginary
parts of the BeurlingAhlfors operator .
Keywords:Fourier multiplier, martingale, laminate Categories:42B15, 60G44, 42B20 

10. CJM 2013 (vol 66 pp. 1050)
 Holmes, Mark; Salisbury, Thomas S.

Random Walks in Degenerate Random Environments
We study the asymptotic behaviour of random walks in i.i.d. random
environments on $\mathbb{Z}^d$. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2valued environment, and show that this does not hold for 3valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong, but nontrivial conditions on the distribution of the environment.
Our results include generalisations (to the nonelliptic setting) of 01 laws for directional transience, and in 2dimensions the existence of a deterministic limiting velocity.
Keywords:random walk, nonelliptic random environment, zeroone law, coupling Category:60K37 

11. CJM 2012 (vol 65 pp. 600)
 Kroó, A.; Lubinsky, D. S.

Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials
We establish asymptotics for Christoffel functions associated with
multivariate orthogonal polynomials. The underlying measures are assumed to
be regular on a suitable domain  in particular this is true if they are
positive a.e. on a compact set that admits analytic parametrization. As a
consequence, we obtain asymptotics for Christoffel functions for measures on
the ball and simplex, under far more general conditions than previously
known. As another consequence, we establish universality type limits in the
bulk in a variety of settings.
Keywords:orthogonal polynomials, random matrices, unitary ensembles, correlation functions, Christoffel functions Categories:42C05, 42C99, 42B05, 60B20 

12. CJM 2011 (vol 64 pp. 1201)
 Aistleitner, Christoph; Elsholtz, Christian

The Central Limit Theorem for Subsequences in Probabilistic Number Theory
Let $(n_k)_{k \geq 1}$ be an increasing sequence of positive integers, and let $f(x)$ be a real function satisfying
\begin{equation}
\tag{1}
f(x+1)=f(x), \qquad \int_0^1 f(x) ~dx=0,\qquad
\operatorname{Var_{[0,1]}}
f \lt \infty.
\end{equation}
If $\lim_{k \to \infty} \frac{n_{k+1}}{n_k} = \infty$
the distribution of
\begin{equation}
\tag{2}
\frac{\sum_{k=1}^N f(n_k x)}{\sqrt{N}}
\end{equation}
converges to a Gaussian distribution. In the case
$$
1 \lt \liminf_{k \to \infty} \frac{n_{k+1}}{n_k}, \qquad \limsup_{k \to \infty} \frac{n_{k+1}}{n_k} \lt \infty
$$
there is a complex interplay between the analytic properties of the
function $f$, the numbertheoretic properties of $(n_k)_{k \geq 1}$,
and the limit distribution of (2).
In this paper we prove that any sequence $(n_k)_{k \geq 1}$ satisfying
$\limsup_{k \to \infty} \frac{n_{k+1}}{n_k} = 1$ contains a nontrivial
subsequence $(m_k)_{k \geq 1}$ such that for any function satisfying
(1) the distribution of
$$
\frac{\sum_{k=1}^N f(m_k x)}{\sqrt{N}}
$$
converges to a Gaussian distribution. This result is best possible: for any
$\varepsilon\gt 0$ there exists a sequence $(n_k)_{k \geq 1}$ satisfying $\limsup_{k \to
\infty} \frac{n_{k+1}}{n_k} \leq 1 + \varepsilon$ such that for every nontrivial
subsequence $(m_k)_{k \geq 1}$ of $(n_k)_{k \geq 1}$ the distribution
of (2) does not converge to a Gaussian distribution for some $f$.
Our result can be viewed as a Ramsey type result: a sufficiently dense
increasing integer sequence contains a subsequence having a certain
requested numbertheoretic property.
Keywords:central limit theorem, lacunary sequences, linear Diophantine equations, Ramsey type theorem Categories:60F05, 42A55, 11D04, 05C55, 11K06 

13. CJM 2011 (vol 64 pp. 1075)
 Raja, Chandiraraj Robinson Edward

A Stochastic Difference Equation with Stationary Noise on Groups
We consider the stochastic difference equation $$\eta _k = \xi _k
\phi (\eta _{k1}), \quad k \in \mathbb Z $$ on a locally compact group $G$
where $\phi$ is an automorphism of $G$, $\xi _k$ are given $G$valued
random variables and $\eta _k$ are unknown $G$valued random variables.
This equation was considered by Tsirelson and Yor on
onedimensional torus. We consider the case when $\xi _k$ have a
common law $\mu$ and prove that if $G$ is a distal group and $\phi$
is a distal automorphism of $G$ and if the equation has a solution,
then extremal solutions of the equation are in oneone
correspondence with points on the coset space $K\backslash G$ for
some compact subgroup $K$ of $G$ such that $\mu$ is supported on
$Kz= z\phi (K)$ for any $z$ in the support of $\mu$. We also provide
a necessary and sufficient condition for the existence of solutions
to the equation.
Keywords:dissipating, distal automorphisms, probability measures, pointwise distal groups, shifted convolution powers Categories:60B15, 60G20 

14. CJM 2011 (vol 64 pp. 961)
 Borwein, Jonathan M.; Straub, Armin; Wan, James; Zudilin, Wadim

Densities of Short Uniform Random Walks
We study the densities of uniform random walks in the plane. A special focus
is on the case of short walks with three or four steps and less completely
those with five steps. As one of the main results, we obtain a hypergeometric
representation of the density for four steps, which complements the classical
elliptic representation in the case of three steps. It appears unrealistic
to expect similar results for more than five steps. New results are also
presented concerning the moments of uniform random walks and, in particular,
their derivatives. Relations with Mahler measures are discussed.
Keywords:random walks, hypergeometric functions, Mahler measure Categories:60G50, 33C20, 34M25, 44A10 

15. CJM 2011 (vol 64 pp. 805)
 Chapon, François; Defosseux, Manon

Quantum Random Walks and Minors of Hermitian Brownian Motion
Considering quantum random walks, we construct discretetime
approximations of the eigenvalues processes of minors of Hermitian
Brownian motion. It has been recently proved by Adler, Nordenstam, and
van Moerbeke that the process of eigenvalues of
two consecutive minors of a Hermitian Brownian motion is a Markov
process; whereas, if one considers more than two consecutive minors,
the Markov property fails. We show that there are analog results in
the noncommutative counterpart and establish the Markov property of
eigenvalues of some particular submatrices of Hermitian Brownian
motion.
Keywords:quantum random walk, quantum Markov chain, generalized casimir operators, Hermitian Brownian motion, diffusions, random matrices, minor process Categories:46L53, 60B20, 14L24 

16. CJM 2011 (vol 64 pp. 869)
 Hu, ZeChun; Sun, Wei

Balayage of SemiDirichlet Forms
In this paper we study the balayage of semiDirichlet forms. We
present new results on balayaged functions and balayaged measures
of semiDirichlet
forms. Some of the results are new even in the Dirichlet forms setting.
Keywords:balayage, semiDirichlet form, potential theory Categories:31C25, 60J45 

17. CJM 2010 (vol 63 pp. 153)
 Hambly, B. M.

Asymptotics for Functions Associated with Heat Flow on the Sierpinski Carpet
We establish the asymptotic behaviour of the partition function, the
heat content, the integrated eigenvalue counting function, and, for
certain points, the ondiagonal heat kernel of generalized
Sierpinski carpets. For all these functions the leading term is of
the form $x^{\gamma}\phi(\log x)$ for a suitable exponent $\gamma$
and $\phi$ a periodic function. We also discuss similar results for
the heat content of affine nested fractals.
Categories:35K05, 28A80, 35B40, 60J65 

18. CJM 2010 (vol 63 pp. 222)
 Wang, JiunChau

Limit Theorems for Additive Conditionally Free Convolution
In this paper we determine the limiting distributional behavior for
sums of infinitesimal conditionally free random variables. We show that the weak
convergence of classical convolution and that of conditionally free convolution
are equivalent for measures in an infinitesimal triangular array,
where the measures may have unbounded support. Moreover, we use these
limit theorems to study the conditionally free infinite divisibility. These results
are obtained by complex analytic methods without reference to the
combinatorics of cfree convolution.
Keywords:additive cfree convolution, limit theorems, infinitesimal arrays Categories:46L53, 60F05 

19. CJM 2010 (vol 63 pp. 104)
 Feng, Shui; Schmuland, Byron; Vaillancourt, Jean; Zhou, Xiaowen

Reversibility of Interacting FlemingViot Processes with Mutation, Selection, and Recombination
Reversibility of the FlemingViot process with mutation, selection,
and recombination is well understood. In this paper, we study the
reversibility of a system of FlemingViot processes that live on a
countable number of colonies interacting with each other through
migrations between the colonies. It is shown that reversibility
fails when both migration and mutation are nontrivial.
Categories:60J60, 60J70 

20. CJM 2009 (vol 61 pp. 1279)
 Hoffman, Christopher; Holroyd, Alexander E.; Peres, Yuval

Tail Bounds for the Stable Marriage of Poisson and Lebesgue
Let $\Xi$ be a discrete set in $\rd$. Call the elements of $\Xi$
{\em centers}. The wellknown Voronoi tessellation partitions
$\rd$ into polyhedral regions (of varying volumes) by allocating
each site of $\rd$ to the closest center. Here we study
allocations of $\rd$ to $\Xi$ in which each center attempts to
claim a region of equal volume $\alpha$.
We focus on the case where $\Xi$ arises from a Poisson process of
unit intensity. In an earlier paper by the authors it was proved that there is a
unique allocation which is {\em stable} in the sense of the
GaleShapley marriage problem. We study the distance $X$ from a
typical site to its allocated center in the stable allocation.
The model exhibits a phase transition in the appetite $\alpha$. In
the critical case $\alpha=1$ we prove a power law upper bound on
$X$ in dimension $d=1$.
(Power law lower bounds were proved earlier
for all $d$). In the noncritical cases
$\alpha<1$ and $\alpha>1$
we prove exponential upper bounds on $X$.
Keywords:stable marriage, point process, phase transition Category:60D05 

21. CJM 2009 (vol 61 pp. 534)
 Chen, ChuanZhong; Sun, Wei

Girsanov Transformations for NonSymmetric Diffusions
Let $X$ be a diffusion process, which is assumed to be
associated with a (nonsymmetric) strongly local Dirichlet form
$(\mathcal{E},\mathcal{D}(\mathcal{E}))$ on $L^2(E;m)$. For
$u\in{\mathcal{D}}({\mathcal{E}})_e$, the extended Dirichlet
space, we investigate some properties of the Girsanov transformed
process $Y$ of $X$. First, let $\widehat{X}$ be the dual process of
$X$ and $\widehat{Y}$ the Girsanov transformed process of $\widehat{X}$.
We give a necessary and sufficient condition for $(Y,\widehat{Y})$ to
be in duality with respect to the measure $e^{2u}m$. We also
construct a counterexample, which shows that this condition may
not be satisfied and hence $(Y,\widehat{Y})$ may not be dual
processes. Then we present a sufficient condition under which $Y$
is associated with a semiDirichlet form. Moreover, we give an
explicit representation of the semiDirichlet form.
Keywords:Diffusion, nonsymmetric Dirichlet form, Girsanov transformation, $h$transformation, perturbation of Dirichlet form, generalized FeynmanKac semigroup Categories:60J45, 31C25, 60J57 

22. CJM 2008 (vol 60 pp. 822)
 Kuwae, Kazuhiro

Maximum Principles for Subharmonic Functions Via Local SemiDirichlet Forms
Maximum principles for subharmonic
functions in the framework of quasiregular local semiDirichlet
forms admitting lower bounds are presented.
As applications, we give
weak and strong maximum principles
for (local) subsolutions of a second order elliptic
differential operator on the domain of Euclidean space under conditions on coefficients,
which partially generalize the results by Stampacchia.
Keywords:positivity preserving form, semiDirichlet form, Dirichlet form, subharmonic functions, superharmonic functions, harmonic functions, weak maximum principle, strong maximum principle, irreducibility, absolute continuity condition Categories:31C25, 35B50, 60J45, 35J, 53C, 58 

23. CJM 2008 (vol 60 pp. 334)
 Curry, Eva

LowPass Filters and Scaling Functions for Multivariable Wavelets
We show that a characterization of scaling functions for
multiresolution analyses given by Hern\'{a}ndez and Weiss and that a
characterization of lowpass filters given by Gundy both hold for
multivariable multiresolution analyses.
Keywords:multivariable multiresolution analysis, lowpass filter, scaling function Categories:42C40, 60G35 

24. CJM 2008 (vol 60 pp. 313)
25. CJM 2008 (vol 60 pp. 457)
 Teplyaev, Alexander

Harmonic Coordinates on Fractals with Finitely Ramified Cell Structure
We define sets with finitely ramified cell structure, which are
generalizations of postcrit8cally finite selfsimilar
sets introduced by Kigami and of fractafolds introduced by Strichartz. In general,
we do not assume even local selfsimilarity, and allow countably many cells
connected at each junction point.
In particular, we consider postcritically infinite fractals.
We prove that if Kigami's resistance form
satisfies certain assumptions, then there exists a weak Riemannian metric
such that the energy can be expressed as the integral of the norm squared
of a weak gradient with respect to an energy measure.
Furthermore, we prove that if such a set can be homeomorphically represented
in harmonic coordinates, then for smooth functions the weak gradient can be
replaced by the usual gradient.
We also prove a simple formula for the energy measure Laplacian in harmonic
coordinates.
Keywords:fractals, selfsimilarity, energy, resistance, Dirichlet forms, diffusions, quantum graphs, generalized Riemannian metric Categories:28A80, 31C25, 53B99, 58J65, 60J60, 60G18 
