On the range of the simple random walk bridge on groups.
On the small maximal flows in first passage percolation
We consider the standard first passage percolation on : with each edge of the lattice we associate a random capacity. We are interested in the maximal flow through a cylinder in this graph. Under some assumptions Kesten proved in 1987 a law of large numbers for the rescaled flow. Chayes and Chayes established that the large deviations far away below its typical value are of surface order, at least for the Bernoulli percolation and cylinders of certain height. Thanks to another approach we extend...
On the smallest eigenvalue of the Stokes operator in a domain with fine-grained random boundary.
On the speed of a planar random walk avoiding its past convex hull
On the Structure of Spatial Branching Processes
The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching...
On the survival time of a duplex system: A Sokhotski-Plemelj problem.
On the tail of the stationary waiting time distribution and limit theorems for the M/G/1 queue
On the Taylor coefficients of the composition of two analytic functions.
On the time constant in a dependent first passage percolation model
We pursue the study of a random coloring first passage percolation model introduced by Fontes and Newman. We prove that the asymptotic shape of this first passage percolation model continuously depends on the law of the coloring. The proof uses several couplings, particularly with greedy lattice animals.
On the total working time of a repaired unit
On the traces of Laguerre processes.
On the vector process obtained by iterated integration of the telegraph signal.
On the virtual waiting time for an retrial queue with two types of calls.
On the waiting time distribution of a cascade queueing process
On the zero-one law and the law of large numbers for random walk in mixing random environment.
On transient queue-size distribution in the batch-arrivals system with a single vacation policy
A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the analysis of...
On truncations for weakly ergodic inhomogeneous birth and death processes
On two fragmentation schemes with algebraic splitting probability
Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with and respectively, for some a > 0. In the first (resp. second) case, since smaller...
On univariate and bivariate aging for dependent lifetimes with Archimedean survival copulas
Let be a pair of exchangeable lifetimes whose dependence structure is described by an Archimedean survival copula, and let denotes the corresponding pair of residual lifetimes after time , with . This note deals with stochastic comparisons between and : we provide sufficient conditions for their comparison in usual stochastic and lower orthant orders. Some of the results and examples presented here are quite unexpected, since they show that there is not a direct correspondence between univariate...
On vacation models with finite capacity.