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Even for bidimensional systems of differential equations the detection of limit cycles by theoretical means is difficult.. The bifurcation theory offers a strong tool for
We prove an extension of the shape result of Blach`ere and Brofferio for Internal Diffusion Limited Aggregation on a wide class of Markov chains on non-amenable graphs..
Briefly, our approach to perfect simulation of a perpetuity from the Vervaat family is to use the Markov-chain-based perfect sampling algorithm known as coupling into and from the
In this note, we study the asymptotic behaviour of Lévy processes with no positive jumps condi- tioned to stay positive and some related processes. In particular, we establish
We prove a finite volume lower bound of the order √ log N on the delocalization of a disordered continuous spin model (resp.. The interaction is assumed to be massless,
Keywords Central Limit Theorem (CLT), Large Deviations Principle (LDP), Markov Pro- cesses, Autoregressive Model (AR1), Positive Recurrent Processes, Martingale Additive Func-
We now construct explicitly a piecewise classical solution for Heaviside initial data that satisfies the Rankine-Hugoniot jump conditions (hence it is a weak solution and will be
In this note, we study the Gaussian fluctuations of the edge occupation measure for a reversible Markov chain and give a nice description of the covariance matrix.. Then we give
