We propose a general method to produce orthogonal polynomial dualities from the∗-
bialgebra structure of Drinfeld–Jimbo quantum groups. The∗-structure allows for the …

We consider a stochastic process of heat conduction where energy is redistributed along a
chain between nearest neighbor sites via an improper beta distribution. Similar to the well …

In this paper we discuss a family of models of particle and energy diffusion on a one-
dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E …

We study self-duality for interacting particle systems, where the particles move as continuous
time random walkers having either exclusion interaction or inclusion interaction. We show …

For a series of Markov processes we prove stochastic duality relations with duality functions
given by orthogonal polynomials. This means that expectations with respect to the original …

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given
data collected at discrete times from a likelihood which is conjugate to the reversible law of …

We examine type D ASEP, a two-species interacting particle system which generalizes the
usual asymmetric simple exclusion process. For certain cases of type D ASEP, the process …

We show that quantum Schur–Weyl duality leads to Markov duality for a variety of
asymmetric interacting particle systems. In particular, we consider the following three …

A reverse duality between the asymmetric simple exclusion process (ASEP) with open
boundary conditions and a biased random walk of a single particle is proved for a special …

We study a class of interacting particle systems with asymmetric interaction showing a self-
duality property. The class includes the ASEP (q, θ), asymmetric exclusion process, with a …