Related papers: Circularly invariant uniformizable probability mea…
We introduce the boolean convolution for probability measures on the unit circle. Roughly speaking, it describes the distribution of the product of two boolean independent unitary random variables. We find an analogue of the characteristic…
A conjecture of Ulam states that the standard probability measure $\pi$ on the Hilbert cube $I^\omega$ is invariant under the induced metric $d_a$ when the sequence $a = \{ a_i \}$ of positive numbers satisfies the condition…
We study some special classes of piecewise continuous maps on a finite smooth partition of a compact manifold and look for invariant measures for such maps. We show that in the simplest one-dimensional case (so-called interval translation…
Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we prove the existence (and conjecture the…
For regime-switching diffusions processes with singular drifts, we introduce integrability conditions involving a nice reference probability measure and the $Q$-matrix of the jump part to study the existence of the invariant probability…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
In this article, we close a gap in the literature by proving existence of invariant measures for reflected SPDEs with only one reflecting barrier. This is done by arguing that the sequence (u(t, .)) is tight in the space of probability…
In this paper, we consider the question of existence and uniqueness of absolutely continuous invariant measures for expanding $C^1$ maps of the circle. This is a question which arises naturally from results which are known in the case of…
We consider a random walk on a closed manifold $M$ driven by a probability measure $\mu$ on the space of $C^2$ diffeomorphisms. Provided $\mu$ has compact support, satisfies certain gap and pinching conditions, and is weak-$*$ close to a…
We introduce the Mass Migration Process (MMP), a conservative particle system on ${\mathbb N}^{{\mathbb Z}^d}$. It consists in jumps of $k$ particles ($k\ge 1$) between sites, with a jump rate depending only on the state of the system at…
Consider piecewise linear Lorenz maps on $[0, 1]$ of the following form \[ f_{a,b,c}(x)= {ll} ax+1-ac & x \in [0, c) b(x-c) & x \in (c, 1].\] We prove that $f_{a,b,c}$ admits an absolutely continuous invariant probability measure (acim)…
We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can…
We prove that for any given modulus of continuity {\omega} there exist (uncountably many) C1 uniformly expanding maps of the circle whose derivatives have $C^1$ as an optimal modulus of continuity and which preserve an invariant probability…
The existence of the weak limit as n --> infinity of the uniform measure on rooted triangulations of the sphere with n vertices is proved. Some properties of the limit are studied. In particular, the limit is a probability measure on random…
We investigate the properties of absolutely continuous invariant probability measures (ACIPs), especially those measures with bounded variation densities, for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps…
The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e.,…
A frequently faced task in experimental physics is to measure the probability distribution of some quantity. Often this quantity to be measured is smeared by a non-ideal detector response or by some physical process. The procedure of…
We study chordal Loewner families in the upper half-plane and show that they have a parametric representation. We show one, that to every chordal Loewner family there corresponds a unique measurable family of probability measures on the…
For a positive number $q$ the Mallows measure on the symmetric group is the probability measure on $S_n$ such that $P_{n,q}(\pi)$ is proportional to $q$-to-the-power-$\mathrm{inv}(\pi)$ where $\mathrm{inv}(\pi)$ equals the number of…
There is only one fully supported ergodic invariant probability measure for the adic transformation on the space of infinite paths in the graph that underlies the Eulerian numbers. This result may partially justify a frequent assumption…