Related papers: A stable Langevin model with diffusive-reflective …
In this paper, we develop a new mathematical technique which allows us to express the joint distribution of a Markov process and its running maximum (or minimum) through the marginal distribution of the process itself. This technique is an…
We show results from simulations of the Langevin dynamics of a two-dimensional scalar model with competing interactions for ultrathin magnetic films. We find a phase transition from a high temperature disordered phase to a low temperature…
In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential.…
We employ an appropriate perturbative scheme in the large viscous regime to study oscillating states in driven Langevin systems. We explicitly determine oscillating state distribution of under-damped Brownian particle subjected to thermal,…
We consider a novel model of stochastic replicator dynamics for potential games that converts to a Langevin equation on a sphere after a change of variables. This is distinct from the models studied earlier. In particular, it is ill-posed…
The individual motion of a colloidal particle is described by an overdamped Langevin equation. When rotational degrees of freedom are relevant, these are described by a corresponding Langevin process. Our purpose is to show that the…
The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying…
Stimulated by experimental progress in high energy physics and astrophysics, the unification of relativistic and stochastic concepts has re-attracted considerable interest during the past decade. Focusing on the framework of special…
We give a probabilistic representation of a one-dimensional diffusion equation where the solution is discontinuous at $0$ with a jump proportional to its flux. This kind of interface condition is usually seen as a semi-permeable barrier.…
The response and nonconserved dynamics of a two-phase interface in the presence of a temperature gradient oriented normally to the interface are considered. Two types of boundary conditions on the order parameter are considered, and the…
Conditioning stable L\'evy processes on zero probability events recently became a tractable subject since several explicit formulas emerged from a deep analysis using the Lamperti transformations for self-similar Markov processes. In this…
Motivated by the notion of isotropic $\alpha$-stable L\'evy processes confined, by reflections, to a bounded open Lipschitz set $D\subset \mathbb{R}^d$, we study some related analytical objects. Thus, we construct the corresponding…
We consider a particle with a Langevin dynamics driven by a uniform non-conservative force, in a one-dimensional potential with periodic boundary conditions. We are interested in the properties of the system for atypical values of the…
We present a novel and rigorous approach to the Langevin dynamics of ideal polymer chains subject to internal distance constraints. The permanent constraints are modelled by harmonic potentials in the limit when the strength of the…
Diffusion models are often introduced from multiple perspectives, such as VAEs, score matching, or flow matching, accompanied by dense and technically demanding mathematics that can be difficult for beginners to grasp. One classic question…
Thermal decay rate over an edge-shaped barrier at high dissipation is studied numerically through the computer modeling. Two sorts of the stochastic Langevin type equations are applied: (i) the Langevin equations for the coordinate and…
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…
We study the linear stability with respect to lateral perturbations of free surface films of polymer mixtures on solid substrates. The study focuses on the stability properties of the stratified and homogeneous steady film states studied in…
We derive general expressions for the free energy, entropy production and entropy extraction rates for a Brownian particle that walks in a viscous medium where the dynamics of its motion is governed by the Langevin equation. It is shown…
We study the exponential convergence to the stationary state for nonequilibrium Langevin dynamics, by a perturbative approach based on hypocoercive techniques developed for equilibrium Langevin dynamics. The Hamiltonian and overdamped…