Metastability of the three dimensional Ising model on a torus at very low temperatures.
Metastable behaviour of small noise Lévy-Driven diffusions
We consider a dynamical system in driven by a vector field -U', where U is a multi-well potential satisfying some regularity conditions. We perturb this dynamical system by a Lévy noise of small intensity and such that the heaviest tail of its Lévy measure is regularly varying. We show that the perturbed dynamical system exhibits metastable behaviour i.e. on a proper time scale it reminds of a Markov jump process taking values in the local minima of the potential U. Due to the heavy-tail nature...
Méthodes probabilistes pour la détermination de résolvantes sous-markoviennes
Méthodes stochastiques pour la détermination de polynômes de Bernstein
Meyer's topology and brownian motion in a composite medium
Micro tangent sets of continuous functions
Motivated by the concept of tangent measures and by H. Fürstenberg’s definition of microsets of a compact set we introduce micro tangent sets and central micro tangent sets of continuous functions. It turns out that the typical continuous function has a rich (universal) micro tangent set structure at many points. The Brownian motion, on the other hand, with probability one does not have graph like, or central graph like micro tangent sets at all. Finally we show that at almost all points Takagi’s...
Mild law of large numbers and its consequences
Minimal moment conditions in the limit theory for general Markov branching processes
Minimal thinness for subordinate Brownian motion in half-space
We study minimal thinness in the half-space for a large class of subordinate Brownian motions. We show that the same test for the minimal thinness of a subset of below the graph of a nonnegative Lipschitz function is valid for all processes in the considered class. In the classical case of Brownian motion this test was proved by Burdzy.
Minimization of the Kullback information for some Markov processes
Minimization of the Kullback information of diffusion processes
Minkowski sums and Brownian exit times
If is a domain in R the Brownian exit time of is denoted by Given domains and in R this paper gives an upper bound of the distribution function of when the distribution functions of and are known. The bound is sharp if and are parallel affine half-spaces. The paper also exhibits an extension of the Ehrhard inequality
Minorantes harmoniques et potentiels - Localisation sur une famille de temps d'arrêt - Réduite forte
est un processus de Markov sur un espace localement compact, et est une fonction excessive. Soit une famille de temps d’arrêt est -harmonique si pour tout , pour tout temps d’arrêt appartenant à . est un potentiel si sa plus grande minorante forte -harmonique est nulle. La plus grande minorante forte -harmonique de est égale à la somme de deux fonctions excessives qui sont étudiées. On déduit différentes caractérisations des -potentiels suivant les propriétés de la famille...
Mixed parametrization for curved exponential models in homogeneous Markov processes with a finite state space.
Mixing time bounds via the spectral profile.
Mixing time for the Ising model : a uniform lower bound for all graphs
Consider Glauber dynamics for the Ising model on a graph of n vertices. Hayes and Sinclair showed that the mixing time for this dynamics is at least nlog n/f(Δ), where Δ is the maximum degree and f(Δ) = Θ(Δlog2Δ). Their result applies to more general spin systems, and in that generality, they showed that some dependence on Δ is necessary. In this paper, we focus on the ferromagnetic Ising model and prove that the mixing time of Glauber dynamics on any n-vertex graph is at least (1/4 + o(1))nlog n....
Mixing time of the Rudvalis shuffle.
Mixing times for Markov chains on wreath products and related homogeneous spaces.
Mixing times for random walks on finite lamplighter groups.
Modeling flocks and prices: Jumping particles with an attractive interaction
We introduce and investigate a new model of a finite number of particles jumping forward on the real line. The jump lengths are independent of everything, but the jump rate of each particle depends on the relative position of the particle compared to the center of mass of the system. The rates are higher for those left behind, and lower for those ahead of the center of mass, providing an attractive interaction keeping the particles together. We prove that in the fluid limit, as the number of particles...