Related papers: On the Brownian directed polymer in a Gaussian ran…
We introduce a new disorder regime for directed polymers in dimension $1+1$ that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter…
We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the…
The problem of Brownian motion in a periodic potential, under the influence of external forcing, which is either random or periodic in time, is studied in this paper. Multiscale techniques are used to derive general formulae for the steady…
Nonlinear stochastic differential equations generating signals with 1/f spectrum have been used so far to describe socio-economical systems. In this paper we consider the motion of a Brownian particle in an inhomogeneous environment such…
Trajectories of an overdamped particle in a highly unstable potential diverge so rapidly, that the variance of position grows much faster than its mean. Description of the dynamics by moments is therefore not informative. Instead, we…
We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensionnal model of active particles. We…
Recent theoretical modeling offers a unified picture for the description of stochastic processes characterized by a crossover from anomalous to normal behavior. This is particularly welcome, as a growing number of experiments suggest the…
Motivated by the study of the directed polymer model with mobile Poissonian traps or catalysts and the stochastic parabolic Anderson model with time dependent potential, we investigate the asymptotic behavior of…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
Explicit density expansions of non-equilibrium probability distribution functions for molecular Brownian particle in ideal gas are obtained in original form what visually implies (is exact solution to) the previously established dynamical…
In this work, we study the dynamics of a single active Brownian particle, as well as the collective behavior of interacting active Brownian particles, in a fluctuating heterogeneous environment. We employ a variant of the diffusing…
One considers the effect of disorder on the 2-dimensional density of states of an electron in a constant magnetic field superposed onto a Poissonnian random distribution of point vortices. If one restricts the electron Hilbert space to the…
We investigate the transport of Brownian particles in a two-dimensional potential under the action of a uniform external force. The potential is periodic in one direction and confines the particle to a narrow channel of varying…
We study a model of interacting random walkers that proposes a simple mechanism for the emergence of cooperation in group of individuals. Each individual, represented by a Brownian particle, experiences an interaction produced by the local…
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication…
We consider the stationary O'Connell-Yor model of semi-discrete directed polymers in a Brownian environment in the intermediate disorder regime and show convergence of the increments of the log-partition function to the energy solutions of…
We study the half-space log-gamma polymer model with stationary initial conditions. We derive exact formulas for the distribution of the partition function along the diagonal across the entire High density phase and Low density phase. We…
We study models for a directed polymer in a random environment (DPRE) in which the polymer traverses a hierarchical diamond graph and the random environment is defined through random variables attached to the vertices. For these models, we…
We consider a system of independent point-like particles performing a Brownian motion while interacting with a Gaussian fluctuating background. These particles are in addition endowed with a discrete two-state internal degree of freedom…
Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation…