Related papers: Effective driven dynamics for one-dimensional cond…
We have shown recently that a Markov process conditioned on rare events involving time-integrated random variables can be described in the long-time limit by an effective Markov process, called the driven process, which is given…
The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…
Large deviation theory provides a framework to understand macroscopic fluctuations and collective phenomena in many-body nonequilibrium systems in terms of microscopic dynamics. In these lecture notes we discuss the large deviation…
In this work, we investigate positive recurrent L\'evy diffusions driven by appropriately scaled Brownian motion and $\alpha$-stable process (with $1<\alpha<2$) in the small noise regime. Supposing that in the vanishing noise limit, our…
In this article, we provide detailed analysis of the long-time behavior of the underdamped Langevin dynamics. We first provide a necessary condition guaranteeing that the zero-noise dynamical system converges to its unique attractor. We…
We consider high-order stochastic processes $x(t)$ described by the Langevin equation $\frac{{{d^m}x\left( t \right)}}{{d{t^m}}}= \sqrt{2D} \xi(t)$, where $\xi(t)$ is a delta-correlated Gaussian noise with zero mean, and $D$ is the strength…
We show that the coarse-grained dynamics model with the time-dependent and fluctuating potential (transient potential) can be derived from the microscopic Hamiltonian dynamics. The concept of the transient potential was first introduced…
We study the dynamics of a single trapped probe surrounded by self-propelled active particles in two dimensions. In the limit of large size separation, we perform an adiabatic elimination of the small active particles to obtain an effective…
The problem of determining dynamical models and trajectories that describe observed time-series data allowing for the understanding, prediction and possibly control of complex systems in nature is of a great interest in a wide variety of…
The nonintegrable Hamiltonian dynamics of particles placed in a symmetric, spatially periodic potential and subjected to a periodically varying field is explored. Such systems can exhibit a rich diversity of unusual transport features. In…
The dynamics of a one-dimensional stochastic system of classical particles consisting of asymmetric death and branching processes is studied. The dynamical activity, defined as the number of configuration changes in a dynamical trajectory,…
Motivated by an application to empirical Bayes learning in high-dimensional regression, we study a class of Langevin diffusions in a system with random disorder, where the drift coefficient is driven by a parameter that continuously adapts…
Motivated to understand the asymptotic behavior of periodically driven thermodynamic systems, we study the prototypical example of Brownian particle, overdamped and underdamped, in harmonic potentials subjected to periodic driving. The…
Motivated by subdiffusive motion of bio-molecules observed in living cells we study the stochastic properties of a non-Brownian particle whose motion is governed by either fractional Brownian motion or the fractional Langevin equation and…
We propose a method to exactly generate bridge run-and-tumble trajectories that are constrained to start at the origin with a given velocity and to return to the origin after a fixed time with another given velocity. The method extends the…
We study the fluctuations of systems modeled by Markov jump processes with periodic generators. We focus on observables defined through time-periodic functions of the system's states or transitions. Using large deviation theory, canonical…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…