Deformed multi-variable Fokker-Planck equations

TL;DR

This paper introduces new multi-variable deformed Fokker-Planck equations linked to RSvD systems, serving as discrete analogs of classical multi-variable FP equations, thus extending the connection between stochastic processes and integrable many-body systems.

Contribution

It presents a novel class of multi-variable deformed Fokker-Planck equations associated with RSvD systems, bridging discrete integrable systems and stochastic differential equations.

Findings

New multi-variable deformed FP equations introduced

Connections established between deformed FP equations and RSvD systems

Framework for discrete deformations of classical FP equations provided

Abstract

In this paper new multi-variable deformed Fokker-Planck (FP) equations are presented. These deformed FP equations are associated with the Ruijsenaars-Schneider-van Diejen (RSvD) type systems in the same way that the usual one variable FP equation is associated with the one particle Schr\"odinger equation. As the RSvD systems are the "discrete" counterparts of the celebrated exactly solvable many-body Calogero-Sutherland-Moser systems, the deformed FP equations presented here can be considered as "discrete" deformations of the ordinary multi-variable FP equations.