Interacting particle systems with sticky boundary

TL;DR

This paper develops stochastic models for interacting particles with sticky boundary behavior in bounded domains, extending solutions to more general initial conditions and applying to particles in chromatography tubes.

Contribution

It introduces a general construction of stochastic dynamics for interacting particles with sticky boundaries, including solutions for singular interactions and broader initial conditions.

Findings

Constructed stochastic dynamics for particles with sticky boundary conditions.

Extended solutions to singular interactions and quasi-everywhere initial points.

Applied model to particles diffusing in chromatography tubes.

Abstract

In this paper, we construct under general assumptions the stochastic dynamics of an interacting particle system in a bounded domain $\Omega$ with sticky boundary. Under appropriate conditions on the interaction the constructed process solves the underlying SDE for every starting point in the state space. Moreover, we also obtain a solution for q.e. starting point in the case of singular interactions which generalizes former results. Finally, the setting is applied to the case of particles diffusing in a chromatography tube.