Related papers: A stable Langevin model with diffusive-reflective …
In this review we present the current state-of-the-art on complex Langevin simulations and their implications for the QCD phase diagram. After a short summary of the complex Langevin method, we present and discuss recent developments. Here…
We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…
In this paper we address the problem of consistently construct Langevin equations to describe fluctuations in non-linear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property together…
In this paper we consider the existence of weakly c\`adl\`ag versions of a solution to a linear equation in a Hilbert space $H$, driven by a Levy process taking values in a Hilbert space $U$. In particular we are interested in diagonal type…
Impulse methods are generalized to a family of integrators for Langevin systems with quadratic stiff potentials and arbitrary soft potentials. Uniform error bounds (independent from stiff parameters) are obtained on integrated positions…
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion…
Recent rapid advances in single particle tracking and supercomputing techniques resulted in an unprecedented abundance of diffusion data exhibiting complex behaviours, such the presence of power law tails of the msd and memory functions,…
In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive…
When is it possible to interpret a given Markov process as a L\'evy-like process? Since the class of L\'evy processes can be defined by the relation between transition probabilities and convolutions, the answer to this question lies in the…
We investigate single-particle diffusion in a two-state Langevin model where the friction coefficient randomly switches between low-friction (liquid-like) and high-friction (glassy-like) states. The dynamics are governed by the ratio…
We introduce a scheme for deriving an optimally-parametrised Langevin dynamics of few collective variables from data generated in molecular dynamics simulations. The drift and the position-dependent diffusion profiles governing the Langevin…
On the basis of general considerations, we propose a Langevin equation accounting for critical phenomena occurring in the presence of two symmetric absorbing states. We study its phase diagram by mean-field arguments and direct numerical…
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay term in the feedback is less than the…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
We propose a solution for linear inverse problems based on higher-order Langevin diffusion. More precisely, we propose pre-conditioned second-order and third-order Langevin dynamics that provably sample from the posterior distribution of…
We study the question whether a possible metastable vacuum state is actually populated in a phase transition in the early universe, as is usually assumed in the discussion of vacuum stability bounds e.g. for Standard Model parameters. A…
Mixing at the interface between a convection zone and an adjacent, stably-stratified layer plays a crucial role in shaping the structure and evolution of stars and planets. In this work, we present a suite of 2D and 3D Boussinesq…
We investigate the possibility of spontaneous supersymmetry breaking in a class of zero-dimensional ${\cal N} = 2$ supersymmetric quantum field theories, with complex actions, using complex Langevin dynamics and stochastic quantization. Our…
We introduce a stochastic equation for the microscopic motion of a tagged particle in the single file model. This equation provides a compact representation of several of the system's properties such as Fluctuation-Dissipation and Linear…
We study large deviations in the Langevin dynamics, with damping of order $\e^{-1}$ and noise of order $1$, as $\e\downarrow 0$. The damping coefficient is assumed to be state dependent. We proceed first with a change of time and then, we…