相关论文: Time change approach to generalized excursion meas…
We prove distributional limit theorems (conditional and integrated) for the occupation times of certain weakly mixing, pointwise dual ergodic transformations at "tied-down" times immediately after "excursions". The limiting random variables…
We prove a quenched local central limit theorem for continuous-time random walks in $\mathbb Z^d, d\ge 2$, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian…
We introduce generalized $(\alpha,\beta)$-transformations, which include all $(\alpha,\beta)$ and generalized $\beta$-transformations, and prove that all transitive generalized $(\alpha,\beta)$-transformations satisfy the level-2 large…
In this paper we prove an estimate for the total variation distance, in the framework of the Breuer-Major theorem, using the Malliavin-Stein method, assuming the underlying function $g$ to be once weakly differentiable with $g$ and $g'$…
We consider $p$ independent Brownian motions in $\R^d$. We assume that $p\geq 2$ and $p(d-2)<d$. Let $\ell_t$ denote the intersection measure of the $p$ paths by time $t$, i.e., the random measure on $\R^d$ that assigns to any measurable…
We investigate a tight binding quantum walk on a graph. Repeated stroboscopic measurements of the position of the particle yield a measured "trajectory", and a combination of classical and quantum mechanical properties for the walk are…
We set observational constraints on the second clock effect, predicted by Weyl unified field theory, by investigating recent data on the dilated lifetime of muons accelerated by a magnetic field. These data were obtained in an experiment…
Central limit theorems for random walks in quenched random environments have attracted plenty of attention in the past years. More recently still, finer local limit theorems -- yielding a Gaussian density multiplied by a highly oscillatory…
A functional approach for the study of the random walks in random sceneries (RWRS) is proposed. Under fairly general assumptions on the random walk and on the random scenery, functional limit theorems are proved. The method allows to study…
We establish general moment estimates for the discrete and continuous exit times of a general It\^o process in terms of the distance to the boundary. These estimates serve as intermediate steps to obtain strong convergence results for the…
We consider the random walk among random conductances on Z^d. We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit…
We study the thermodynamic formalism for generalized Gibbs measures, such as renormalization group transformations of Gibbs measures or joint measures of disordered spin systems. We first show existence of the relative entropy density and…
The generalized grey Brownian motion is a time continuous self-similar with stationary increments stochastic process whose one dimensional distributions are the fundamental solutions of a stretched time fractional differential equation.…
In this note we first consider local times of random walks killed at leaving positive half-axis. We prove that the distribution of the properly rescaled local time at point $N$ conditioned on being positive converges towards an exponential…
It is shown that in systems with time-dependent and/or spatially nonuniform temperature $T(t,x)$, (i) most of the transport processes is weakly non-ergodic, and (ii) the diffusion (Brownian motion, BM) is anomalous. A few examples of simple…
As a sequel to (Berman, 2008a), we show that the rotation of the Universe can be dealt by generalised Gaussian metrics, defined in this paper. Robertson-Walker's metric has been employed with proper-time, in its standard applications; the…
We complete the program developed in our previous works aiming to construct an infinite sequence of invariant measures of gaussian type associated with the conservation laws of the Benjamin-Ono equation.
For a smooth stationary Gaussian field on $\mathbb{R}^d$ and level $\ell \in \mathbb{R}$, we consider the number of connected components of the excursion set $\{f \ge \ell\}$ (or level set $\{f = \ell\}$) contained in large domains. The…
We prove a quenched central limit theorem for balanced random walks in time dependent ergodic random environments which is not necessarily nearest-neigbhor. We assume that the environment satisfies appropriate ergodicity and ellipticity…
We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at $0$ whenever they cross that point. We show that the perturbed random walk, after being…