Related papers: Markov Duality for Stochastic Six Vertex Model
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 that orthogonal self-dualities arise from unitary…
We study the stochastic six-vertex model in half-space with generic integrable boundary weights, and define two families of multivariate rational symmetric functions. Using commutation relations between double-row operators, we prove a skew…
We study three classes of continuous time Markov processes (inclusion process, exclusion process, independent walkers) and a family of interacting diffusions (Brownian energy process). For each model we define a boundary driven process…
Stochastic convergence of discrete time Markov processes has been analysed based on a dual Lyapunov approach. Using some existing results on ergodic theory of Markov processes, it has been shown that existence of a properly subinvariant…
We present a theorem which elucidates the connection between self-duality of Markov processes and representation theory of Lie algebras. In particular, we identify sufficient conditions such that the intertwining function between two…
We introduce a new, algebraic method to construct duality functions for integrable dynamic models. This method will be implemented on dynamic stochastic higher spin vertex models, where we prove the duality functions are the $ _3 \varphi_2$…
The notion of Markov duality between two Markov processes that can live in two different configurations spaces $(x,{\tilde x})$ is revisited via the spectral decompositions of the two Markov generators in their bi-orthogonal basis of right…
We obtain a new multiple integral representation for the spin-spin correlation functions of the XXZ spin-1/2 infinite chain. We show that this representation is closely related with the partition function of the six-vertex model with domain…
We obtain a new representation for the partition function of the six vertex model with domain wall boundaries using a functional equation recently derived by the author. This new representation is given in terms of a sum over the…
We obtain stochastic duality functions for specific Markov processes using representation theory of Lie algebras. The duality functions come from the kernel of a unitary intertwiner between $*$-representations, which provides (generalized)…
Consider a system $X = ((x_\xi(t)), \xi \in \Omega_N)_{t \geq 0}$ of interacting Fleming-Viot diffusions with mutation and selection which is a strong Markov process with continuous paths and state space $(\CP(\I))^{\Omega_N}$, where $\I$…
We study two generalizations of the asymmetric simple exclusion process with two types of particles. Particles of type 1 can jump over particles of type 2, while particles of type 2 can only influence the jump rates of particles of type 1.…
In this paper we introduce a model which provides a new approach to the phenomenon of stochastic resonance. It is based on the study of the properties of the stationary distribution of the underlying stochastic process. We derive the…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…
We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible…
We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample…
In this paper, we use the matrix model of pure fundamental flavors (without the adjoint field) to check the Seiberg duality in the case of complete mass deformation. We show that, by explicit integration at both sides of electric and…
Given a semi-Markov law, using an additional parameter, we consider a family of stochastic flows corresponding to that law. Then we suitably select a particular flow, for which we obtain expressions of the meeting and merging probabilities…
We investigate duality in entanglement of a bipartite multi-photon system generated from a coherent state of light. The system can exhibit polarization entanglement if the two parts are distinguished by their parity, or parity entanglement…
We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(sl_2)$ $R$-matrix and…