相关论文: Sensitivity to switching rates in stochastically s…

We study the eigenvalue distribution of a random matrix, at a transition where a new connected component of the eigenvalue density support appears away from other connected components. Unlike previously studied critical points, which…

We deal with a complex-valued Ornstein-Uhlenbeck (OU) process with parameter $\lambda\in\mathbb{R}$starting from a point different from 0 and the way that it winds around the origin.The starting point of this paper is the skew product…

The dynamical quantum phase transition is characterized by the emergence of nonanalytic behaviors in the rate function, corresponding to the occurrence of exact zero points of the Loschmidt echo in the thermodynamical limit. In general,…

For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

The purpose of this paper is to provide a complete description of the eigenvalues of the generator of a neutral multi-type Moran model, and the applications to the study of the speed of convergence to stationarity. The Moran model we…

We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization…

In this paper, we introduce a class of processes that contains many natural examples. The interesting feature of such type processes lays on its infinite memory that allows it to record a quite ancient history. Then, using the martingale…

We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…

We explain and exploit the random matrix formulation of the Loschmidt echo for the XX spin chain, valid for multiple domain wall initial states and also for a XX spin chain generalized with additional interactions to more neighbours. For…

In cases where the same real-world system can be modeled both by an ODE system $\bD$ and a Boolean system $\bB$ it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively…

This article studies Markovian stochastic motion of a particle on a graph with finite number of nodes and periodically time-dependent transition rates that satisfy the detailed balance condition at any time. We show that under general…

We present a convergence result for infinite products of stochastic matrices with positive diagonals. We regard infinity of the product to the left. Such a product converges partly to a fixed matrix if the minimal positive entry of each…

Time-irreversible stochastic processes are frequently used in natural sciences to explain non-equilibrium phenomena and to design efficient stochastic algorithms. Our main goal in this thesis is to analyse their dynamics by means of large…

For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…

In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov processes obtained as the unique mild solution to stochastic…

We construct a class of nonnegative martingale processes that oscillate indefinitely with high probability. For these processes, we state a uniform rate of the number of oscillations and show that this rate is asymptotically close to the…

We consider boundary value problems for stochastic differential equations of second order with a small parameter. For this case we prove a special existence and unicity theorem for strong solutions. The asymptotic behavior of these…

This article develops a general framework for Laplace duality between positive Markov processes in which the one-dimensional Laplace transform of one process can be represented through that of another. We show that a process admits a…

We study a class of interacting particle systems on $\mathbb{R}$ which was recently investigated by F. G\"otze and the second author [GV14]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different…