Related papers: TASEP and generalizations: Method for exact soluti…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
Motivated by the normal form of a fast-slow ordinary differential equation exhibiting a pitchfork singularity we consider the discrete-time dynamical system that is obtained by an application of the explicit Euler method. Tracking…
We study the totally asymmetric exclusion process (TASEP) on a finite one-dimensional lattice with open boundaries, i.e., in contact with two reservoirs at different potentials. The total (time-integrated) current through the system is a…
We study a problem with three equivalent formulations: describing Gibbs measures for five-vertex model in quadrant; classifying coherent systems on a p-deformation of the Gelfand-Tsetlin graph related to Grothendieck polynomials; finding…
Although an intimate relation between entropy and diffusion has been advocated for many years and even seems to have been verified in theory and experiments, a quantitatively reliable study, and any derivation of an algebraic relation…
In the current work we present two generalizations of the Parallel Tempering algorithm, inspired by the so-called continuous-time Infinite Swapping algorithm. Such a method, found its origins in the molecular dynamics community, and can be…
Statistical inference can be seen as information processing involving input information and output information that updates belief about some unknown parameters. We consider the Bayesian framework for making inferences about dynamical…
We study reaction-diffusion particle systems with several interaction mechanisms. As the number of particles tends to infinity, the system admits a mean-field limit describing the bulk behaviour. We focus on determining the propagation…
Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the…
These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the…
Asynchronous event sequence clustering aims to group similar event sequences in an unsupervised manner. Mixture models of temporal point processes have been proposed to solve this problem, but they often suffer from overfitting, leading to…
We consider the asymmetric simple exclusion process (ASEP) on $\mathbb{Z}$. For continuous densities, ASEP is in local equilibrium for large times, at discontinuities however, one expects to see a dynamical phase transition, i.e. a mixture…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs)…
The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process, recently introduced by Matetski, Quastel, Remenik (arXiv:1701.00018), that describes the limit fluctuations of the height function associated to the totally asymmetric simple…
We consider a large class of deformations of continuous and discrete biorthogonal ensembles and investigate their behavior in the limit of a large number of particles. We provide sufficient conditions to ensure that if a biorthogonal…
We consider the $q$-totally asymmetric simple exclusion process ($q$-TASEP) in the stationary regime and study the fluctuation of the position of a particle. We first observe that the problem can be studied as a limiting case of an…
The aim of this paper is to establish a causal link between the policies implemented by technology companies and the outcomes they yield within intricate temporal and/or spatial dependent experiments. We propose a novel…