Work

Quantitative low-temperature spectral asymptotics for reversible diffusions in temperature-dependent domains

Year: 2026

Type: article

Abstract: We derive novel low-temperature asymptotics for the spectrum of the infinitesimal generator of the overdamped Langevin dynamics. The novelty is that this operator is endowed with homogeneous Dirichlet conditions at the boundary of a domain which depends on the temperature. From the point of view of stochastic processes, this gives information on the long-time behavior of the diffusion conditioned on non-absorption at the boundary, in the so-called quasistationary regime. Our results provide precise estimates of the spectral gap and principal eigenvalue, extending the Eyring–Kramers formula. The phenomenology is richer than in the case of a fixed boundary and gives new insight into the sensitivity of the spectrum with respect to the shape of the domain near critical points of the energy function. Our work is motivated by the optimization of accelerated molecular dynamics algorithms (such as Parallel Replica dynamics), where optimal state definitions naturally vary with the temperature.

Source: Journal de Mathématiques Pures et Appliquées

DOI: 10.1016/j.matpur.2026.103996

Authors: Noé Blassel, Tony Lelièvre, Gabriel Stoltz

Institutions: Institut national de recherche en sciences et technologies du numérique, École nationale des ponts et chaussées, CERMICS, Institut Polytechnique de Paris, MATHERIALS: MATHematics for MatERIALS

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,900

Funders: European Commission, Agence Nationale de la Recherche, European Research Council