Work

Planted directed polymer: Inferring a random walk from noisy images

Year: 2025

Type: article

Abstract: We introduce and study the planted directed polymer, in which the path of a random walker is inferred from noisy "images" accumulated at each time step. Formulated as a nonlinear problem of Bayesian inference for a hidden Markov model, this problem is a generalization of the directed polymer problem of statistical physics, coinciding with it in the limit of zero signal to noise. For a one-dimensional walker we present numerical investigations and analytical arguments that no phase transition is present. When formulated on a Cayley tree, methods developed for the directed polymer are used to show that there is a transition with decreasing signal to noise where effective inference becomes impossible, meaning that the average fractional overlap between the inferred and true paths falls from one to zero.

Source: Physical review. E

DOI: 10.1103/physreve.111.024135

Authors: Sun Woo P. Kim, Austen Lamacraft

Institutions: King's College London, University of Cambridge

Language: English

Topic: Theoretical and Computational Physics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Funder: Engineering and Physical Sciences Research Council

Awards: Theoretical Condensed Matter Cambridge - Critical Mass Grant, DTP 2224 King's College London, G6240949451