Related papers: Self-duality of Markov processes and intertwining …
We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases: (1) Using a Schur-Weyl duality between a two-parameter quantum group and a…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
We construct a four parameter (z, z', a, b) family of Markov dynamics that preserve the z-measures on the boundary of the branching graph for classical Lie groups of type B, C, D. Our guiding principle is the "method of intertwiners" used…
Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a…
Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials associated with Calogero-Sutherland type…
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 marginal law of the diffusion, when a generic dual process on a…
We prove a intertwining relation (or Markov duality) between the $(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP, two discrete time Markov chains introduced by Povolotsky. Using this and a variant of the coordinate Bethe ansatz we…
The aim of this paper is to study differential and spectral properties of the infinitesimal operator of two dimensional Markov processes with diffusion and discrete components. The infinitesimal operator is now a second-order differential…
We present novel equivalences in random matrix and tensor models between complex and self-adjoint theories with nontrivial quadratic terms in the action, established through an intermediate field representation. More precisely, we show that…
The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential…
Graphical models have proven to be powerful tools for representing high-dimensional systems of random variables. One example of such a model is the undirected graph, in which lack of an edge represents conditional independence between two…
We consider a Markov chain of point processes such that each state is a super position of an independent cluster process with the previous state as its centre process together with some independent noise process. The model extends earlier…
We study a time-non-homogeneous Markov process which arose from free probability, and which also appeared in the study of stochastic processes with linear regressions and quadratic conditional variances. Our main result is the explicit…
We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…
Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are first introduced by means of suitable Doob…
In this paper, we study one dimensional Markov processes with spatial delay. Since the seminal work of Feller, we know that virtually any one dimensional, strong, homogeneous, continuous Markov process can be uniquely characterized via its…
We present an algebraic study of a kind of quantum systems belonging to a family of superintegrable Hamiltonian systems in terms of shape-invariant intertwinig operators, that span pairs of Lie algebras like $(su(n),so(2n))$ or…
In this thesis, we generalize the Koszul duality for associative algebras and operads to PROPs. The operads are algebraic objects that represent the operations with multiple inputs but only one output acting on a certain type of algebras. A…
We introduce and study the permanence properties of the class of linear transfers between probability measures. This class contains all cost minimizing mass transports, but also martingale mass transports, the Schrodinger bridge associated…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…