Related papers: The dual Burnside process
We demonstrate exciting similarities between classical and quantum many body systems whose microscopic dynamics are composed of non-reciprocal three-site facilitated exclusion processes. We show that the quantum analogue of the classical…
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…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
A time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are…
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization of a given Poisson group) we provide functorial recipes to…
Let $Mat_{\mathbb{C}}(K,N)$ be the space of $K\times N$ complex matrices. Let $\mathbf{B}_t$ be Brownian motion on $Mat_{\mathbb{C}}(K,N)$ starting from the zero matrix and $\mathbf{M}\in Mat_{\mathbb{C}}(K,N)$. We prove that, with $K\ge…
In the context of Markov processes, we show a new scheme to derive dual processes and a duality function based on a boson representation. This scheme is applicable to a case in which a generator is expressed by boson creation and…
We develop the theory of strong stationary duality for diffusion processes on compact intervals. We analytically derive the generator and boundary behavior of the dual process and recover a central tenet of the classical Markov chain theory…
The double Burnside $R$-algebra $\text{B}_R(G,G)$ of a finite group $G$ with coefficients in a commutative ring $R$ has been introduced by S. Bouc. It is $R$-linearly generated by finite $(G,G)$-bisets, modulo a relation identifying…
A coinless quantisation procedure of continuous and discrete time Birth and Death (BD) processes is presented. The quantum Hamiltonian H is derived by similarity transforming the matrix L describing the BD equation in terms of the square…
We consider Markov processes of cubic stochastic (in a fixed sense) matrices which are also called quadratic stochastic process (QSPs). A QSP is a particular case of a continuous-time dynamical system whose states are stochastic cubic…
Bosonic two-mode squeezed states are paradigmatic entangled Gaussian states that have wide utility in quantum information and metrology. Here, we show that the basic structure of these states can be generalized to arbitrary bipartite…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
The perturbed GUE corners ensemble is the joint distribution of eigenvalues of all principal submatrices of a matrix $G+\mathrm{diag}(\mathbf{a})$, where $G$ is the random matrix from the Gaussian Unitary Ensemble (GUE), and…
The quantum duality Principle of Drinfel'd states that any quantization ${\mathcal{G}}_{\hbar}$ of a Poisson-Lie group $\mathcal{G}$ should be dual as a quantum group to a quantization $\mathcal{G}^*_{\hbar}$ of the Poisson dual group…
This article presents a concrete mathematical framework for the generation of entangled quantum states from classical stochastic processes. We demonstrate that any density operator $\rho_{AB}$ of a composite system can be derived from the…
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum…
We study the stirring process with $N-1$ species on a generic graph $G=(V,\mathcal{E})$ with reservoirs. The multispecies stirring process generalizes the symmetric exclusion process, which is recovered in the case $N=2$. We prove the…
In this paper, we develop an in-depth analysis of non-reversible Markov chains on denumerable state space from a similarity orbit perspective. In particular, we study the class of Markov chains whose transition kernel is in the similarity…
This article gives sharp estimates for the mixing time of the Burnside process for Sylow $p$-double cosets in the symmetric group $S_n$. This process is a Markov chain on $S_n$ which can be used to uniformly sample Sylow $p$-double cosets.…