Dérivabilité du plus grand exposant caractéristique des produits de matrices aléatoires indépendantes à coefficients positifs
Dérive des marches aléatoires et théorèmes limites
Discrete Löwner evolution
Discrete Models of Time-Fractional Diffusion in a Potential Well
Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour for time tending to infinity...
Discrete random processes with memory: Models and applications
The contribution focuses on Bernoulli-like random walks, where the past events significantly affect the walk's future development. The main concern of the paper is therefore the formulation of models describing the dependence of transition probabilities on the process history. Such an impact can be incorporated explicitly and transition probabilities modulated using a few parameters reflecting the current state of the walk as well as the information about the past path. The behavior of proposed...
Distributions of functionals of diffusions with jumps.
Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model
Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph and is more likely to cross edges it has visited before. We show that it can be represented in terms of a vertex-reinforced jump process (VRJP) with independent gamma conductances; the VRJP was conceived by Werner and first studied by Davis and Volkov [10, 11], and is a continuous-time process favouring sites with more local time. We calculate,...
Empilements de cercles et théorème de Liouville (d'après T. Dubejko)
Ensemble de première visite d'une promenade aléatoire à un convexe
Equidistant sampling for the maximum of a Brownian motion with drift on a finite horizon.
Ergodic and Mixing Random Walks on Locally Compact Groups.
Ergodic behaviour of “signed voter models”
We answer some questions raised by Gantert, Löwe and Steif (Ann. Inst. Henri Poincaré Probab. Stat.41(2005) 767–780) concerning “signed” voter models on locally finite graphs. These are voter model like processes with the difference that the edges are considered to be either positive or negative. If an edge between a site and a site is negative (respectively positive) the site will contribute towards the flip rate of if and only if the two current spin values are equal (respectively opposed)....
Errata: A Matrix with an application to the motion of an absorbing Markov chain. I.
Erratum / Correction to : “A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement”
Erratum to : “Green kernel estimates and the full Martin boundary for random walks on lamplighter groups and Diestel–Leader graphs”
Estimates for interval probabilities of the sums of random variables with locally subexponential distributions.
Estimates for simple random walks on fundamental groups of surfaces
Numerical estimates are given for the spectral radius of simple random walks on Cayley graphs. Emphasis is on the case of the fundamental group of a closed surface, for the usual system of generators.
Estimates for the distribution of sums and maxima of sums of random variables without the Cramér condition.
Estimates in the invariance principle in terms of truncated power moments.
Estimates of random walk exit probabilities and application to loop-erased random walk.