Related papers: Limit theorems for the tagged particle in exclusio…
The idea of a parsing of a stationary process according to a collection of words is introduced, and the basic framework required for the asymptotic analysis of these parsings is presented. We demonstrate how the pointwise ergodic theorem…
We study a continuous-time simple random walk on a regular rooted tree of depth $n$ in two settings: either the walk is started from a leaf vertex and run until the tree root is first hit or it is started from the root and run until it has…
We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…
Let ${Z_{n},n\geq 0} $ be a critical branching process in random environment and let $T$ be its moment of extinction. Under the annealed approach we prove, as $n\to \infty ,$ a limit theorem for the number of particles in the process at…
This paper investigates the birth-death ("B-D" for short) process on tree with continuous time, emphasizing on estimating the principal eigenvalue (equivalently, the convergence rate) of the process with Dirichlet boundary at the unique…
We consider an $n$-tuple of independent ergodic Markov processes, each of which converges (in the sense of separation distance) at an exponential rate, and obtain a necessary and sufficient condition for the $n$-tuple to exhibit a…
We consider the random conductance model, where the underlying graph is an infinite supercritical Galton--Watson tree, the conductances are independent but their distribution may depend on the degree of the incident vertices. We prove that,…
It has recently been shown that there are substantial differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the existence of diffusion local time.…
A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…
We investigate the randomized decision tree complexity of a specific class of read-once threshold functions. A read-once threshold formula can be defined by a rooted tree, every internal node of which is labeled by a threshold function…
We present two limit theorems, a mean ergodic and a central limit theorem, for a specific class of one-dimensional diffusion processes that depend on a small-scale parameter $\varepsilon$ and converge weakly to a homogenized diffusion…
We study Random Walks in an i.i.d. Random Environment (RWRE) defined on $b$-regular trees. We prove a functional central limit theorem (FCLT) for transient processes, under a moment condition on the environment. We emphasize that we make no…
We consider an exclusion process representing a reactive dynamics of a pulled front on the integer lattice, describing the dynamics of first class $X$ particles moving as a simple symmetric exclusion process, and static second class $Y$…
In this paper we extend two limit theorems which were recently obtained for fragmentation processes to such processes with immigration. More precisely, in the setting with immigration we consider a limit theorem for the process counted with…
Place an active particle at the root of a $d$-ary tree and a single dormant particle at each non-root site. In discrete time, active particles move towards the root with probability $p$ and, otherwise, away from the root to a uniformly…
Under certain mild conditions, limit theorems for additive functionals of some $d$-dimensional self-similar Gaussian processes are obtained. These limit theorems work for general Gaussian processes including fractional Brownian motions,…
Consider a $d$-ary rooted tree ($d\geq3$) where each edge $e$ is assigned an i.i.d. (bounded) random variable $X(e)$ of negative mean. Assign to each vertex $v$ the sum $S(v)$ of $X(e)$ over all edges connecting $v$ to the root, and assume…
We prove a strong form of the equivalence of ensembles for the invariant measures of zero range processes conditioned to a supercritical density of particles. It is known that in this case there is a single site that accomodates a…
We show that the growth of a unimodular random rooted tree $(T,o)$ of degree bounded by $d$ always exists, assuming its upper growth passes the critical threshold $\sqrt{d-1}$. This complements Timar's work who showed the possible…
We obtain pointwise ergodic theorems with rate under conditions expressed in terms of the convergence of series involving $\|\sum_{k=1} ^nf\circ \theta^k\|_2$, improving previous results. Then, using known results on martingale…