arXiv subjects

Amine Asselah

Publications and source records attributed to Amine Asselah.

41 records · Page 3Linked to original sources

arXiv2005

Self-Intersection Times for Random Walk, and Random Walk in Random Scenery in dimensions d>4

We consider Random Walk in Random Scenery, denoted $X_n$, where the random walk is symmetric on $Z^d$, with $d>4$, and the random field is made up of i.i.d random variables with a stretched exponential tail decay, with exponent $α$ with $1<α$. We present asymptotics for the probability, over both randomness, that $\{X_n>n^β\}$ for $1/2<β<1$. To obtain such asymptotics, we establish large deviations estimates for the the self-intersection local times process.

math.PR↗

arXiv2005

Hitting times for special patterns in the symmetric exclusion process on Z^d

We consider the symmetric exclusion process {η_t,t>0} on {0,1}^{Z^d}. We fix a pattern A:={η:\sum_Λη(i)\ge k}, where Λis a finite subset of Z^d and k is an integer, and we consider the problem of establishing sharp estimates for τ, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for τin a simple way. Also, we characterize the trajectories {η_s,s\le t} conditioned on {τ>t}.

math.PR↗

arXiv2005

A note on random walk in random scenery

We consider a d-dimensional random walk in random scenery X(n), where the scenery consists of i.i.d. with exponential moments but a tail decay of the form exp(-c t^a) with a ny}. We show that this probability is of order exp(-(ny)^b) with b=a/(a+1).

math.PR↗

arXiv2003

On the Dirichlet problem for asymmetric zero-range process on increasing domains

We characterize the principal eigenvalue of the generator of the asymmetric zero-range process in dimensions d>2, with Dirichlet boundary on special domains. We obtain a Donsker-Varadhan variational representation for the principal eigenvalue, and show that the corresponding eigenfunction is unique in a natural class of functions. This allows us to obtain asymptotic hitting time estimates.

math.PR↗

arXiv2001

Regularity of quasi-stationary measures for simple exclusion in dimension d >= 5

We consider the symmetric simple exclusion process on Z^d, for d>= 5, and study the regularity of the quasi-stationary measures of the dynamics conditionned on not occupying the origin. For each ρ\in ]0,1[, we establish uniqueness of the density of quasi-stationary measures in L^2(d\nur), where \nur is the stationary measure of density ρ. This, in turn, permits us to obtain sharp estimates for P_{\nur}(τ>t), where τis the first time the origin is occupied.

math.PR↗