Related papers: The random average process and random walk in a sp…
Random walks as well as diffusions in random media are considered. Methods are developed that allow one to establish large deviation results for both the `quenched' and the `averaged' case.
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
We present a methodology for the study of the dispersion of trajectories of stochastic processes in reconstructed phase spaces from observed data. The methodology allows to find ensembles of analog states, i.e. states that are close in the…
An overview is given of recent advances in nonequilibrium statistical mechanics about the statistics of random paths and current fluctuations. Although statistics is carried out in space for equilibrium statistical mechanics, statistics is…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop…
The evolution of many stochastic systems is accurately described by random walks on graphs. We here explore the close connection between local steady-state fluctuations of random walks and the global structure of the underlying graph.…
We consider a system of multiscale stochastic differential equations whose slow component is drivenby a fractional Brownian motion with Hurst parameter H greater than 1/2. Under ergodic assumptions ensuring the applicability of the…
Fluctuations of energy and heat are investigated during the relaxation following the instantaneous temperature quench of an extended system. Results are obtained analytically for the Gaussian model and for the large $N$ model quenched below…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
We study the angular process related to random walks in the Euclidean and in the non-Euclidean space where steps are Cauchy distributed. This leads to different types of non-linear transformations of Cauchy random variables which preserve…
Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but also allows fluctuation measurements which may reveal the structure and dynamics of the underlying biochemical network.…
Temporal fluctuations in the Hadamard walk on circles are studied. A temporal standard deviation of probability that a quantum random walker is positive at a given site is introduced to manifest striking differences between quantum and…
We study a class of discrete-time random walks in $\mathbb{R}^d$ whose conditional drift decays polynomially in time and grows polynomially with the distance from the origin to the current position. This class is related to several models…
We study the average shape of a fluctuation of a time series x(t), that is the average value <x(t)-x(0)>_T before x(t) first returns, at time T, to its initial value x(0). For large classes of stochastic processes we find that a scaling law…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with an external environment under sequences of quantum measurements performed at random times.…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
We describe a universal transition mechanism characterizing the passage to an annealed behavior and to a regime where the fluctuations about this behavior are Gaussian, for the long time asymptotics of the empirical average of the expected…
Elephant random walk is a kind of one-dimensional discrete-time random walk with infinite memory: For each step, with probability $\alpha$ the walker adopts one of his/her previous steps uniformly chosen at random, and otherwise he/she…