Probabilistic Interpretation of the Calder\'on Problem

TL;DR

This paper offers a probabilistic perspective on Calderón's inverse conductivity problem by employing symmetric Dirichlet forms to relate it to reflecting diffusion processes and boundary trace processes.

Contribution

It introduces a novel probabilistic interpretation of the inverse conductivity problem using the framework of symmetric Dirichlet forms.

Findings

Provides a probabilistic framework for Calderón's problem

Connects inverse conductivity with reflecting diffusion processes

Lays groundwork for new analytical techniques in inverse problems

Abstract

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calder\'{o}n's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.