Stochastic dynamics macroscopically governed by the porous medium equation for isothermal flow.
Stochastic foundations of the universal dielectric response
We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...
Stochastic integral by a semi-Markov process of diffusion type.
Stochastic model of accelerated testing methods of fatigue
Stochastic queue core problem with an efficient length on a tree network
In this paper, we consider a stochastic queue core () problem on a tree network, aiming to identify a path , called the core, in an environment system. Let be a tree network, the problem on involves finding a core , with an optimal length, that minimizes the total weighted travel time from all vertices to the core as well as the average response time to the customer demands. We assume that a mobile server traverses the core to provide services to customers, while customers move to their...
Stochastic reaction diffusion equations and interacting particle systems
Stochastische Bewegungen und ihre ersten Integrale.
Stoghastig behavior of an intermittently used system
Strict convexity of the limit shape in first-passage percolation.
Strong hydrodynamic limit for attractive particle systems on .
Strong law of large numbers for the interface in ballistic deposition
Study of Queuing Systems with a Generalized Departure Process
This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based...
Study of the Iterations of a Mapping Associated to a Spin Glass Model
Study of the stability of the queueing network of Lu-Kumar-Bramson by the fluid limit method. (Étude par la méthode des limites fluides de la stabilité du réseau de file d'attente de Lu-Kumar-Bramson.)
Subdiffusive behavior of random walk on a random cluster
Substable and pseudo-isotropic processes. Connections with the geometry of subspaces of [Book]
Supercritical self-avoiding walks are space-filling
In this article, we consider the following model of self-avoiding walk: the probability of a self-avoiding trajectory between two points on the boundary of a finite subdomain of is proportional to . When is supercritical (i.e. where is the connective constant of the lattice), we show that the random trajectory becomes space-filling when taking the scaling limit.
Superdiffusivity for brownian motion in a poissonian potential with long range correlation I: Lower bound on the volume exponent
We study trajectories of -dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential is constructed from a field of traps whose centers location is given by a Poisson Point Process and whose radii are IID distributed with a common distribution that has unbounded support; it has the particularity of having long-range correlation. We focus on the case where the law of the trap radii has power-law decay and prove that superdiffusivity...
Superdiffusivity for brownian motion in a poissonian potential with long range correlation II: Upper bound on the volume exponent
This paper continues a study on trajectories of Brownian Motion in a field of soft trap whose radius distribution is unbounded. We show here that for both point-to-point and point-to-plane model the volume exponent (the exponent associated to transversal fluctuation of the trajectories) is strictly less than and give an explicit upper bound that depends on the parameters of the problem. In some specific cases, this upper bound matches the lower bound proved in the first part of this work and...
Sur la charge associée à une mesure aléatoire réelle stationnaire