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In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so…

In this paper, we establish two different results. The first result is a characterization theorem saying that if the stationary state probabilities for originally described Markovian discriminatory processor sharing (DPS) system have a…

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

We introduce and study the class of linear transfers between probability distributions and the dual class of Kantorovich operators between function spaces. Linear transfers can be seen as an extension of convex lower semi-continuous…

We provide a nonasymptotic analysis of convergence to stationarity for a collection of Markov chains on multivariate state spaces, from arbitrary starting points, thereby generalizing results in [Khare and Zhou Ann. Appl. Probab. 19 (2009)…

Eulerian polynomials record the distribution of descents over permutations. Caylerian polynomials likewise record the distribution of descents over Cayley permutations, where a Cayley permutation is a word of positive integers such that if…

We introduce the theory of normal ordered grammars, which gives a natural generalization of the normal ordering problem. To illustrate the main idea, we explore normal ordered grammars associated with the Eulerian polynomials and the…

In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…

Many examples of exactly solvable birth and death processes, a typical stationary Markov chain, are presented together with the explicit expressions of the transition probabilities. They are derived by similarity transforming exactly…

Markov cohort state-transition models have been the standard approach for simulating the prognosis of patients or, more generally, the life trajectories of individuals over a time period. Current approaches for estimating the variance of a…

Physical systems that dissipate, mix and develop turbulence also irreversibly transport statistical density. In statistical physics, laws for these processes have a mathematical form and tractability that depends on whether the description…

We introduce quantum Markov categories as a structure that refines and extends a synthetic approach to probability theory and information theory so that it includes quantum probability and quantum information theory. In this broader…

We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the $m$-dimensional lattice and for which the $m$ matrices that record the…

In low temperature limit, we study electron counting statistics of a disordered conductor. We derive an expression for the distribution of charge transmitted over a finite time interval by using a result from the random matrix theory of…

We analyze the properties of degree-preserving Markov chains based on elementary edge switchings in undirected and directed graphs. We give exact yet simple formulas for the mobility of a graph (the number of possible moves) in terms of its…

The asymmetric simple exclusion process (ASEP) is a model for translation in protein synthesis and traffic flow; it can be defined as a Markov chain describing particles hopping on a one-dimensional lattice. In this article I give an…

This paper develops the theory and methods for modeling a stationary count time series via Gaussian transformations. The techniques use a latent Gaussian process and a distributional transformation to construct stationary series with very…

We study the full counting statistics of current of large open systems through the application of random matrix theory to transition-rate matrices. We develop a method for calculating the ensemble-averaged current-cumulant generating…

Numerical Generalized Randomized Hamiltonian Monte Carlo is introduced, as a robust, easy to use and computationally fast alternative to conventional Markov chain Monte Carlo methods for continuous target distributions. A wide class of…

Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C,…