Related papers: Effective dynamics of a conditioned generalized li…
We consider a one-dimensional microscopic reaction-diffusion process obtained as a superposition of a Glauber and a Kawasaki dynamics. The reaction term is tuned so that a dynamical phase transition occurs in the model as a suitable…
We consider the performance of Glauber dynamics for the random cluster model with real parameter $q>1$ and temperature $\beta>0$. Recent work by Helmuth, Jenssen and Perkins detailed the ordered/disordered transition of the model on random…
We study the Langevin dynamics of diffusive particles with regular pairwise interactions under mean-field scaling. By approximating empirical distributions with conditional distributions, we establish coercive and contractive properties for…
The diffusion equation is the primary tool to study the movement dynamics of a free Brownian particle, but when spatial heterogeneities in the form of permeable interfaces are present, no fundamental equation has been derived. Here we…
We consider a model of a dynamical Lorentz gaz : a single particle is moving in $\mathbb{R}^d$ through an array of fixed an soft scatterers each possessing an internal degree of freedom coupled to the particle. Assuming the initial velocity…
We identify a new scenario for dynamical phase transitions associated with time-integrated observables occurring in diffusive systems described by the macroscopic fluctuation theory. It is characterized by the pairwise meeting of first- and…
We introduce a general framework for deriving effective dynamics from arbitrary time-dependent generators, based on a systematic operator cumulant expansion. Unlike traditional approaches, which typically assume periodic or adiabatic…
An ensemble of classical subsystems interacting with surrounding particles has been considered. In general case, a phase volume of the subsystems ensemble was shown to be a function of time. The evolutional equations of the ensemble are…
This work presents a general thermodynamic approach to describe particle diffusion on a lattice, a model used to study transport processes in solids and on surfaces. By treating each lattice site as an open thermodynamic system, the effects…
A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…
This paper investigates the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of $N$ interacting point particles, where the time evolution of the joint distribution…
Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…
We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanisms (Glauber dynamics). Previous results…
The wavefunction of a single spin system in a prepared initial state evolves to equilibrium with a heat bath. The average spin $$q(t) = p_{\uparrow}(t) - p_{\downarrow}(t)$$ exhibits a characteristic time for this evolution. With the proper…
Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
Time dependent signals in experimental techniques such as Nuclear Magnetic Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an ensemble average over many microscopical dynamical processes. While there are a number of…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…