Last passage percolation in macroscopically inhomogeneous media.
Laws of the iterated logarithm for the brownian snake
Likely path to extinction in simple branching models with large initial population.
Limit laws for the energy of a charged polymer
In this paper we obtain the central limit theorems, moderate deviations and the laws of the iterated logarithm for the energy Hn=∑1≤j<k≤nωjωk1{Sj=Sk} of the polymer {S1, …, Sn} equipped with random electrical charges {ω1, …, ωn}. Our approach is based on comparison of the moments between Hn and the self-intersection local time Qn=∑1≤j<k≤n1{Sj=Sk} run by the d-dimensional random walk {Sk}. As partially needed for our main objective and partially motivated by their independent interest,...
Limit theorem in the space of continuous functions for the Dirichlet polynomial related with the Riemann zeta-funtion
A limit theorem in the space of continuous functions for the Dirichlet polynomialwhere denote the coefficients of the Dirichlet series expansion of the function in the half-plane
Limit theorems for self-normalized large deviation.
Limit theorems in the boundary hitting problem for a multidimensional random walk.
Linear speed large deviations for percolation clusters.
Long-time behavior of solutions to a class of quasilinear parabolic equations with random coefficients
Lower deviation probabilities for supercritical Galton–Watson processes
Lower large deviations and laws of large numbers for maximal flows through a box in first passage percolation
We consider the standard first passage percolation model in ℤd for d≥2. We are interested in two quantities, the maximal flow τ between the lower half and the upper half of the box, and the maximal flow ϕ between the top and the bottom of the box. A standard subadditive argument yields the law of large numbers for τ in rational directions. Kesten and Zhang have proved the law of large numbers for τ and ϕ when the sides of the box are parallel to the coordinate hyperplanes: the two variables grow...
Lower large deviations for the maximal flow through tilted cylinders in two-dimensional first passage percolation
Equip the edges of the lattice ℤ2 with i.i.d. random capacities. A law of large numbers is known for the maximal flow crossing a rectangle in ℝ2 when the side lengths of the rectangle go to infinity. We prove that the lower large deviations are of surface order, and we prove the corresponding large deviation principle from below. This extends and improves previous large deviations results of Grimmett and Kesten [9] obtained for boxes of particular orientation.
Lyapunov exponents for the one-dimensional parabolic Anderson model with drift.
Matchings and the variance of Lipschitz functions
We are interested in the rate function of the moderate deviation principle for the two-sample matching problem. This is related to the determination of 1-Lipschitz functions with maximal variance. We give an exact solution for random variables which have normal law, or are uniformly distributed on the Euclidean ball.
Maxima of the cells of an equiprobable multinomial.
Mesures de Gibbs sur les Cantor réguliers
Mesures dominantes et théorème de Sanov
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...
Minimization of the Kullback information for some Markov processes
Minimization of the Kullback information of diffusion processes