Dynamic Random Walks on Motion Groups

TL;DR

This paper introduces the first study of dynamic random walks on the motion group, providing convergence results and extending classical limit theorems to inhomogeneous Markov chains with time-dependent transitions.

Contribution

It presents original convergence results for products of independent random elements in the motion group and extends classical limit theorems to dynamic, inhomogeneous Markov chains.

Findings

Convergence results for products of random elements in the motion group.

Extension of Central Limit and Local Limit theorems to dynamic random walks.

New results for mutually commuting rotations.

Abstract

In this note, we give an original convergence result for products of independent random elements of motion group. Then we consider dynamic random walks which are inhomogeneous Markov chains whose transition probability of each step is, in some sense, time dependent. We show, briefly, how Central Limit theorem and Local Limit theorems can be derived from the classical case and provide new results when the rotations are mutually commuting. To the best of our knowledge, this work represents the first investigation of dynamic random walks on the motion group.