English
Related papers

Related papers: Fluctuations for fully pushed stochastic fronts

200 papers

The quantum jump approach, where pairs of state vectors follow Stochastic Schroedinger Equation (SSE) in order to treat the exact quantum dynamics of two interacting systems, is first described. In this work the non-uniqueness of such…

Quantum Physics · Physics 2009-02-05 Denis Lacroix

In this work, we introduce a new method to prove the existence and uniqueness of a variational solution to the stochastic nonlinear diffusion equation $dX(t)={\rm div} [\frac{\nabla X(t)}{|\nabla X(t)|}]dt+X(t)dW(t) in…

Probability · Mathematics 2018-06-27 Michael Röckner , Viorel Barbu

In this paper, we investigate the existence and finite-time blow-up for the solution of a reaction-diffusion system of semilinear stochastic partial differential equations (SPDEs) subjected to a two-dimensional fractional Brownian motion…

Analysis of PDEs · Mathematics 2024-05-28 S. Sankar , Manil T. Mohan , S. Karthikeyan

We consider a nonlinear differential equation under the combined influence of small state-dependent Brownian perturbations of size $\varepsilon$, and fast periodic sampling with period $\delta$; $0<\varepsilon, \delta \ll 1$. Thus, state…

Probability · Mathematics 2022-05-20 Shivam Dhama , Chetan D. Pahlajani

We consider the motion of a particle under a continuum random environment whose distribution is given by the Howitt-Warren flow. In the moderate deviation regime, we establish that the quenched density of the motion of the particle (after…

Probability · Mathematics 2024-12-24 Sayan Das , Hindy Drillick , Shalin Parekh

We propose new limiting dynamics for stochastic gradient descent in the small learning rate regime called stochastic modified flows. These SDEs are driven by a cylindrical Brownian motion and improve the so-called stochastic modified…

Probability · Mathematics 2023-02-15 Benjamin Gess , Sebastian Kassing , Vitalii Konarovskyi

We study interface fluctuations for the $1$D stochastic Allen-Cahn equation perturbed by half a spatial derivative of the spacetime white noise. This half derivative makes the solution distribution-valued, so that proper renormalization is…

Probability · Mathematics 2025-08-22 Weijun Xu , Shuhan Zhou

Many approaches to modelling reaction-diffusion systems with anomalous transport rely on deterministic equations and ignore fluctuations arising due to finite particle numbers. Starting from an individual-based model we use a…

Statistical Mechanics · Physics 2019-05-29 Joseph W. Baron , Tobias Galla

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Numerical Analysis · Mathematics 2021-06-30 Yukun Li , Shuonan Wu , Yulong Xing

We consider the $[0,1]$-valued solution $(u_{t,x}:t\geq 0, x\in \mathbb R)$ to the one dimensional stochastic reaction diffusion equation with Wright-Fisher noise \[\partial_t u= \partial_x^2 u + f(u) + \epsilon \sqrt{u(1-u)} \dot W.\]…

Probability · Mathematics 2023-03-23 Clayton Barnes , Leonid Mytnik , Zhenyao Sun

We study transport of an inertial Brownian particle moving in a symmetric and periodic one-dimensional potential, and subjected to both a symmetric, unbiased external harmonic force as well as biased dichotomic noise $\eta(t)$ also known as…

Statistical Mechanics · Physics 2016-06-22 J. Spiechowicz , J. Luczka , L. Machura

We present comprehensive numerical studies of the motion of a buoyant or a nearly neutrally buoyant nano-sized ellipsoidal particle in a fluid filled cylindrical tube without or with the presence of imposed pressure gradient (weak…

Computational Physics · Physics 2017-06-07 N. Ramakrishnan , Y. Wang , D. M. Eckmann , P. S. Ayyaswamy , Ravi Radhakrishnan

In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…

Analysis of PDEs · Mathematics 2025-02-05 Mark van den Bosch , Christian H. S. Hamster , Hermen Jan Hupkes

We investigate the fluctuations of cumulative density of particles in the asymmetric simple exclusion process with respect to the stationary distribution (also known as the steady state), as a stochastic process indexed by $[0,1]$. In three…

Probability · Mathematics 2019-12-30 Włodzimierz Bryc , Yizao Wang

Recently it has been shown that when an equation that allows so-called pulled fronts in the mean-field limit is modelled with a stochastic model with a finite number $N$ of particles per correlation volume, the convergence to the speed…

Statistical Mechanics · Physics 2009-11-07 Debabrata Panja

A new asymptotic method is presented for the analysis of the traveling waves in the one-dimensional reaction-diffusion system with the diffusion with a finite velocity and Kolmogorov-Petrovskii-Piskunov kinetics. The analysis makes use of…

Statistical Mechanics · Physics 2007-05-23 Sergei Fedotov

Inspired by [Fehrman, Gess; Invent. Math., 2023], we provide a fine analysis of the McKean-Vlasov PDE with singular interactions and drift terms of square root form. As the corresponding skeleton equation of Dean-Kawasaki equation with…

Probability · Mathematics 2024-07-29 Zhengyan Wu , Rangrang Zhang

We study the asymptotics of Allen-Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise). The conclusion is that the long time, large space behavior of the solutions is…

Analysis of PDEs · Mathematics 2019-09-13 Pierre-Louis Lions , Panagiotis E. Souganidis

The purpose of this paper is to establish a well-posedness theory for conservative stochastic partial differential equations on the whole space. This class of stochastic PDEs arises in fluctuating hydrodynamics, and includes the…

Probability · Mathematics 2024-10-02 Benjamin Fehrman , Benjamin Gess

A quantitatively reliable theoretical description of the dynamics of fluctuations in non-equilibrium is indispensable in the experimental search for the QCD critical point by means of ultra-relativistic heavy-ion collisions. In this work we…

Nuclear Theory · Physics 2019-06-26 Marlene Nahrgang , Marcus Bluhm , Thomas Schaefer , Steffen A. Bass