Représentation géométrique de la fonction arc tang
Note sur la parabole
The number of absorbed individuals in branching brownian motion with a barrier
We study supercritical branching Brownian motion on the real line starting at the origin and with constant drift . At the point , we add an absorbing barrier, i.e. individuals touching the barrier are instantly killed without producing offspring. It is known that there is a critical drift , such that this process becomes extinct almost surely if and only if . In this case, if denotes the number of individuals absorbed at the barrier, we give an asymptotic for as goes to infinity. If ...
An electromagnetic free-boundary problem
Chains with complete connections and one-dimensional Gibbs measures.
Large deviations for voter model occupation times in two dimensions
We study the decay rate of large deviation probabilities of occupation times, up to time , for the voter model : ℤ×[0, ∞)→{0, 1} with simple random walk transition kernel, starting from a Bernoulli product distribution with density ∈(0, 1). In [ (1988) 401–413], Bramson, Cox and Griffeath showed that the decay rate order lies in [log(), log()]. In this paper, we establish the true decay rates depending on the level. We show that the decay rates are log() when the deviation from ...
Recherches sur les surfaces réglées tétraédrales symétriques
Atlas de 52 Planches Partie 2
Une martingale de saut multiplicatif donné
Modèles solubles en mécanique statistique
Ergodic behaviour of “signed voter models”
We answer some questions raised by Gantert, Löwe and Steif ( (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).
Sur la structure de certaines familles de tribus
Atlas de 46 Planches Partie 3
Atlas de 55 Planches Partie 1
Variétés algébriques en mécanique statistique
Intermittency on catalysts: three-dimensional simple symmetric exclusion.
Intermittency on catalysts: symmetric exclusion.
From holonomy of the Ising model form factors to -fold integrals and the theory of elliptic curves.
The parabolic Anderson model in a dynamic random environment: Basic properties of the quenched Lyapunov exponent
In this paper we study the parabolic Anderson equation , , , where the -field and the -field are -valued, is the diffusion constant, and is the discrete Laplacian. The -field plays the role of athat drives the equation. The initial condition , , is taken to be non-negative and bounded. The solution of the parabolic Anderson equation describes the evolution of a field of particles performing independent simple random walks with binary branching: particles jump at rate , split into two...
Renormalization, isogenies, and rational symmetries of differential equations.
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