Related papers: Poisson boundary of $GL_d(\Q)$

A random geometric graph $G(\mathcal{X}_n, r_n)$ is formed by taking a binomial process $\mathcal{X}_n$ as the set of vertices and joining any two distinct points with an edge if they lie within distance $r_n$ of each other. We investigate…

In the random graph $G(n,p)$ with $pn$ bounded, the degrees of the vertices are almost i.i.d Poisson random variables with mean $\gl:= p(n-1)$. Motivated by this fact, we introduce the Poisson cloning model $G_{PC} (n,p)$ for random graphs…

We prove a normal form theorem for Poisson structures around Poisson transversals (also called cosymplectic submanifolds), which simultaneously generalizes Weinstein's symplectic neighborhood theorem from symplectic geometry and Weinstein's…

The greedy walk is a deterministic walk that always moves from its current position to the nearest not yet visited point. In this paper we consider the greedy walk on an inhomogeneous Poisson point process on the real line. Our primary…

We investigate convolution semigroups of probability measures with continuous densities on locally compact abelian groups, which have a discrete subgroup such that the factor group is compact. Two interesting examples of the quotient…

Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of…

This paper is concerned with the Lyapunov spectrum for measurable cocycles over an ergodic pmp system taking values in semi-simple real Lie groups. We prove simplicity of the Lyapunov spectrum and its continuity under certain perturbations…

Let $\Gamma$ be a Gromov hyperbolic group, endowed with an arbitrary left-invariant hyperbolic metric, quasi-isometric to a word metric. The action of $\Gamma$ on its boundary $\partial\Gamma$ endowed with the Patterson-Sullivan measure…

We introduce a Lie bialgebra structure on the central extension of the Lie algebra of differential operators on the line and the circle (with scalar or matrix coefficients). This defines a Poisson--Lie structure on the dual group of…

We study random walks on groups of isometries of non-proper delta-hyperbolic spaces under the assumption that at least one element in the group satisfies Bestvina-Fujiwara's WPD condition. We show that in this case typical elements are WPD,…

We consider the distribution of spacings between consecutive elements in subsets of Z/qZ where q is highly composite and the subsets are defined via the Chinese remainder theorem. We give a sufficient criterion for the spacing distribution…

Motivated by a conjecture that doubled four-dimensional Chern-Simons produces new integrable models, we perform its Hamiltonian analysis and find the theory's Poisson algebra. This requires carefully accounting for a set of boundary…

Consider a sequence of independent random isometries of Euclidean space with a previously fixed probability law. Apply these isometries successively to the origin and consider the sequence of random points that we obtain this way. We prove…

We consider a random walk among a Poisson system of moving traps on ${\mathbb Z}$. In earlier work [DGRS12], the quenched and annealed survival probabilities of this random walk have been investigated. Here we study the path of the random…

We study the number of isolated nodes in a soft random geometric graph whose vertices constitute a Poisson process on the torus of length L (the line segment [0,L] with periodic boundary conditions), and where an edge is present between two…

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…

We propose an aproach for asymptotic analysis of plane partition statistics related to counts of parts whose sizes exceed a certain suitably chosen level. In our study, we use the concept of conjugate trace of a plane partition of the…

In this paper, we study random walks on groups that contain superlinear divergent geodesics, in the line of thoughts of Goldsborough-Sisto. The existence of a superlinear divergent geodesic is a quasi-isometry invariant which allows us to…

The topology of the Bowditch boundary of a relatively hyperbolic group pair gives information about relative splittings of the group. It is therefore interesting to ask if there is generic behavior of this boundary. The purpose of this…