Related papers: An Example of Intrinsic Randomness in Deterministi…
We pursue our study of integrable weak noise theories of directed polymer and interacting particle stochastic models in the 1D KPZ universality class. Here we focus on the $q$-TASEP in either continuous or discrete time. Each particle on…
We study dynamical Galerkin schemes for evolutionary partial differential equations (PDEs), where the projection operator changes over time. When selecting a subset of basis functions, the projection operator is non-differentiable in time…
Burgers' equation is an important mathematical model used to study gas dynamics and traffic flow, among many other applications. Previous analysis of solutions to Burgers' equation shows an infinite stream of simple poles born at t = 0^+,…
Stochastic partial differential equations (SPDEs) have become a crucial ingredient in a number of models from economics and the natural sciences. Many SPDEs that appear in such applications include non-globally monotone nonlinearities.…
An important functional of Poisson random measure is the negative binomial process (NBP). We use NBP to introduce a generalized Poisson-Kingman distribution and its corresponding random discrete probability measure. This random discrete…
In this paper, we study backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP in short) with non-Lipschitz coefficients on random time interval. The probabilistic interpretation for the…
We theoretically study the Totally Asymmetric Exclusion Process (TASEP) with quenched jumping rates disorder and finite lifetime chain. TASEP is widely used to model the translation of messenger RNAs by Ribosomes in protein synthesis. Since…
Recently, progress has been made in the theory of turbulence, which provides a framework on how a deterministic process changes to a stochastic one owing to the change in thermodynamic states. It is well known that, in the framework of…
We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory…
We use exponential asymptotic analysis to identify the relevance of Stokes' phenomenon to integrability in discrete systems. We study Stokes' phenomenon in two discrete problems with the same (leading-order) continuous limit, a…
We define a new variant of exclusion processes in discrete time that has jump probabilities that depend on the last jump performed. In a particular limit for the jump probabilities and in suitable scaling limits for space and time, we…
We introduce two new exactly solvable (stochastic) interacting particle systems which are discrete time versions of q-TASEP. We call these geometric and Bernoulli discrete time q-TASEP. We obtain concise formulas for expectations of a large…
Using the Bethe ansatz we obtain in a determinant form the exact solution of the master equation for the conditional probabilities of the totally asymmetric exclusion process with particle-dependent hopping rates on Z. From this we derive a…
This paper studies the 1D pressureless turbulence (the Burgers equation). It shows that reliable numerics in this problem is very easy to produce if one properly discretizes the Burgers equation. The numerics it presents confirms the 7/2…
Although many computational methods for rare event sampling exist, this type of calculation is not usually practical for general nonequilibrium conditions, with macroscopically irreversible dynamics and away from both stationary and…
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as interval variable, mass belief function in Dempster-Shafer theory…
We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by $a\geq0$, which creates a shock in the particle density of order $aT^{-1/3},$ $T$ the observation time. When starting from step initial data,…
We investigate the current properties in the totally asymmetric simple exclusion process (TASEP) on a quenched random energy landscape. In low- and high-density regimes, the properties are characterized by single-particle dynamics. In the…
We study an inhomogenous multispecies version of the Totally Asymmetric Simple Exclusion Process (TASEP) on a periodic oriented one dimensional lattice, which depends on two sets of parameters $({\bf \tau},{\bf \nu})$, attached to the…
We revisit the defect-induced nonequilibrium phase transition from a largely homogeneous free-flow phase to a phase-separated congested phase in the sublattice totally asymmetric simple exclusion process (TASEP) with local deterministic…