Internal Control of The Transition Kernel for Stochastic Lattice Dynamics

TL;DR

This paper introduces a novel geometric combinatorial approach to control the transition kernel in stochastic lattice dynamics, advancing the understanding of controlling kinetic equations in complex systems.

Contribution

It presents a new geometric combinatorial method for controlling the transition kernel in stochastic lattice dynamics, which is a significant advancement over previous approaches.

Findings

Established paths for controls using the new geometric combinatorial argument.

Demonstrated control of the transition kernel in the kinetic limit.

Extended control techniques from harmonic chains to stochastic lattice systems.

Abstract

In [5], we have designed impulsive and feedback controls for harmonic chains with a point thermostat. In this work, we study the internal control for stochastic lattice dynamics, with the goal of controlling the transition kernel of the kinetic equation in the limit. A major novelty of the work is the introduction of a new geometric combinatorial argument, used to establish paths for the controls.