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Preprint Oct 2026

Central limit theorem for the Smoluchowski--Kramers approximation

We establish the central limit theorem (CLT) for Smoluchowski--Kramers approximation of Langevin equations with state-dependent, possibly non-symmetric friction and multiplicative noise. To the best of our knowledge, this is the first such result, even in the case of constant friction and additive noise. The result dif...

Yun Li, Long-Jie Xie, Li Yang et al. · 0 citations
Preprint Sep 2026

Stochastic fractional diffusion equations with spatial Gaussian noise in the Stratonovich regime

For a class of stochastic fractional diffusion equations, we prove the existence of Stratonovich solutions and obtain the precise values of the Lyapunov exponents governing the large $t$-asymptotics of their $p$-th moments for all real $p\in\{1\}\cup[2,\infty)$, as well as the large $p$-asymptotics of the $p$-th moment...

Yu-Hui Guo, Jian Song, Guan-Yu Wu · 0 citations
Preprint Sep 2026

Long-time asymptotics of nonlinear Fokker-Planck equations with inhomogeneous diffusion and natural boundary conditions

In this paper, we study the long-time asymptotics for nonlinear Fokker-Planck equations with spatial inhomogeneous diffusion, based on the law of energy dissipation. First, we derive a priori positive lower and upper bounds for solutions of the equations. Next, we give a sufficient condition for deriving the exponentia...

K. Araki, Masashi Mizuno · 0 citations
Preprint Sep 2026

Spectral theory for dynamical large deviations in non-Markov self-interacting processes

We develop a spectral theory for dynamical large deviations in non-Markov jump processes and non-Markov chains, whose dynamics depends on the past through state- and jump-dependent empirical observables. We demonstrate that a multiscale Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) Ansatz separates fast configurational rel...

Francesco Coghi, J. P. Garrahan · 0 citations
Preprint Oct 2026

Reversible Stratonovich perturbations for accelerating convergence to equilibrium of Langevin dynamics

In this paper, we study the problem of sampling from a probability distribution using Langevin-type dynamics. We consider overdamped Langevin dynamics perturbed by adding a Stratonovich perturbation that preserves reversibility. We prove an optimal scaling for the Stratonovich perturbation applied to Gaussian target di...

Guillaume Louis, G. Pavliotis, G. Vilmart · 0 citations
Preprint Aug 2026

Equilibrium fluctuations of the weakly asymmetric inclusion process

We prove that the stationary density fluctuation field of the one-dimensional weakly asymmetric simple inclusion process converges to the energy solution of the stochastic Burgers equation. The key technical ingredient is a second-order Boltzmann-Gibbs principle tailored to the microscopic current. As a consequence, we...

Simon Gabriel · 0 citations

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