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We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…

Probability · Mathematics 2010-11-08 Magda Peligrad , Wei Biao Wu

In this paper, we establish the well-posedness of stochastic heat equations on moving domains, which amounts to a study of infinite dimensional interacting systems. The main difficulty is to deal with the problems caused by the time-varying…

Probability · Mathematics 2023-01-25 Tianyi Pan , Wei Wang , Jianliang Zhai , Tusheng Zhang

Stochastic thermodynamics is a framework for describing non-equilibrium processes at the level of fluctuating trajectories, where the state of a system evolves as a stochastic time series, allowing thermodynamic quantities such as work,…

The classic central limit theorem and $\alpha$-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case of probabilistic independence of the…

Statistical Mechanics · Physics 2008-05-04 Sabir Umarov , Constantino Tsallis , Murray Gell-Mann , Stanly Steinberg

We consider two continuous It\^o semimartingales observed with noise and sampled at stopping times in a nonsynchronous manner. In this article we establish a central limit theorem for the pre-averaged Hayashi-Yoshida estimator of their…

Statistics Theory · Mathematics 2013-07-04 Yuta Koike

The aim of this paper is the rigorous derivation of a stochastic non-linear diffusion equation from a radiative transfer equation perturbed with a random noise. The proof of the convergence relies on a formal Hilbert expansion and the…

Analysis of PDEs · Mathematics 2014-05-13 Arnaud Debussche , Sylvain De Moor , Julien Vovelle

We give sharp conditions for the large time asymptotic simplification of aggregation-diffusion equations with linear diffusion. As soon as the interaction potential is bounded and its first and second derivatives decay fast enough at…

Analysis of PDEs · Mathematics 2021-05-28 José A. Carrillo , David Gómez-Castro , Yao Yao , Chongchun Zeng

We present a new stochastic analysis for steady and transient one-dimensional heat conduction problem based on the homogenization approach. Thermal conductivity is assumed to be a random field K consisting of random variables of a total…

Statistical Mechanics · Physics 2018-09-05 Zhijie Xu

Starting from a master equation in a quantum Hamiltonian form and a coupling to a heat bath we derive an evolution equation for a collective hopping process under the influence of a stochastic energy landscape. There results different…

Statistical Mechanics · Physics 2009-10-31 Michael Schulz , Steffen Trimper

Consider "Frozen Random Walk" on $\mathbb{Z}$: $n$ particles start at the origin. At any discrete time, the leftmost and rightmost $\lfloor{\frac{n}{4}}\rfloor$ particles are "frozen" and do not move. The rest of the particles in the "bulk"…

Probability · Mathematics 2015-09-02 Laura Florescu , Shirshendu Ganguly , Yuval Peres , Joel Spencer

We consider a class of Gibbs measures defined with respect to increments $\{\omega(t)-\omega(s)\}_{s<t}$ of $d$-dimensional Wiener measure, with the underlying Hamiltonian carrying interactions of the form $H(t-s,\omega(t)-\omega(s))$ that…

Probability · Mathematics 2021-07-27 Chiranjib Mukherjee

Diffusive transport of a particle in spatially correlated random energy landscape having exponential density of states has been considered. We exactly calculate the diffusivity in the nondispersive quasi-equilibrium transport regime and…

Disordered Systems and Neural Networks · Physics 2018-02-14 S. V. Novikov

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

Probability · Mathematics 2009-11-11 V. Shcherbakov

We derive the hydrodynamic limit of a kinetic equation with a stochastic, short range perturbation of the velocity operator. Under some mixing hypotheses on the stochastic perturbation, we establish a diffusion-approximation result: the…

Analysis of PDEs · Mathematics 2020-10-01 Nils Caillerie , Julien Vovelle

We establish a quenched local central limit theorem for the dynamic random conductance model on $\mathbb{Z}^d$ only assuming ergodicity with respect to space-time shifts and a moment condition. As a key analytic ingredient we show H\"older…

Probability · Mathematics 2021-05-28 Sebastian Andres , Alberto Chiarini , Martin Slowik

We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…

Analysis of PDEs · Mathematics 2021-10-12 Mohamed Ghattassi , Xiaokai Huo , Nader Masmoudi

We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat, $Q$, flowing across the oscillator in a time interval $\tau$ is a stochastic variable…

Statistical Mechanics · Physics 2013-05-29 Keiji Saito , Abhishek Dhar

The stochastic efficiency of effusion as a thermal engine is investigated within the framework of stochastic thermodynamics. Explicit results are obtained for the probability distribution of the efficiency both at finite times and in the…

Statistical Mechanics · Physics 2015-02-10 Karel Proesmans , Bart Cleuren , Christian Van Den Broeck

The diffusion equation and its time-fractional counterpart can be obtained via the diffusion limit of continuous-time random walks with exponential and heavy-tailed waiting time distributions. The space dependent variable-order…

Statistical Mechanics · Physics 2025-10-24 Christopher N. Angstmann , Daniel S. Han , Bruce I. Henry , Boris Z. Huang , Zhuang Xu

Limit theorems are proved for quadratic forms of Gaussian random fields in presence of long memory. We obtain a non central limit theorem under a minimal integrability condition, which allows isotropic and anisotropic models. We apply our…

Statistics Theory · Mathematics 2010-01-08 Frédéric Lavancier , Anne Philippe