Stochastic processes and conformal invariance

TL;DR

This paper explores a one-dimensional fluctuating interface model with a dynamic exponent of 1, revealing a connection between conformal field theory and stochastic processes, and analyzing avalanche behaviors and finite-size scaling.

Contribution

It establishes a rigorous link between conformal field theory and stochastic interface models with non-local desorption processes.

Findings

Finite-size scaling of average height and interface width

Avalanche size distribution obeys finite-size scaling with new exponents

Connection between CFT and stochastic processes in interface dynamics

Abstract

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent $z=1$. The events that occur are adsorption, which is local, and desorption which is non-local and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the $c=0$ conformal field theory of percolation. This implies in a rigorous way a connection between CFT and stochastic processes. The finite-size scaling behavior of the average height, interface width and other observables are obtained. The avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents.