Research
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Research
Research
6,849+ open-access research outputs.
Many stochastic systems are built by wiring typed components together, but the wiring is often neither purely sequential nor type-homogeneous. This paper develops categorical semantics for such system…
Upon the introduction of the Metropolis algorithm, the question of how many steps in the Markov chain were needed to achieve convergence to stationarity became apparent. The convergence was rather slo…
We consider the symmetric Markov random flight $\bold X(t), \; t>0,$ in the Euclidean space $\Bbb R^m, \; m\ge 3$, performed by a particle that moves in $\Bbb R^m$ with constant finite speed and chang…
This article extends weak convergence bounds of Markov transition kernels to convergence bounds on the variance of the Markov kernel applied to Lipschitz functions. In the reversible case, weak conver…
We derive a general scheme to construct infinitely many probabilistic counterparts for solutions to nonlinear PDEs by recasting the latter as different nonlinear Fokker--Planck equations and by constr…
Deterministic-scan and random-scan component-wise Markov chain Monte Carlo algorithms, such as Gibbs samplers and conditional Metropolis-Hastings, are popular approaches for sampling from multivariate…
We introduce the notion of uniform exactness, or uniform amenability at infinity, for discrete groups and prove it for a wide class of groups containing free groups and their limit groups. This shows …
Markov chain Monte Carlo (MCMC) methods provide powerful framework for sampling unknown probability measures across a wide range of scientific applications. In some settings, the target distribution i…
We establish the weak large deviations principle for empirical measures of Markov chains on $\mathbb R^d$ under mild assumptions. In particular, no irreducibility is assumed and the initial measure ma…
The cross-ratio degree problem is about counting rational curves with $n$ marked points satisfying $n-3$ cross-ratio conditions. This problem has a tropical analogue which provides the same number, as…
We present a simple construction of hat tilings. The construction can be carried out by superimposing a triangular grid on a specially colored image and reading off the orientation of the tiles. We sh…
We establish a higher-dimensional irrationality criterion for periods which are presented as Mellin integrals depending on many parameters. The criterion is stated as an upper bound on the multi-varia…
The sequentially Markov coalescent (SMC) is a Markov jump process which models correlations in local genealogies across a chromosome. It has been used as a theoretical tool for studying linkage disequ…
The first paper in this series introduced a \emph{short-to-long mixing} condition that captures mean-field GOE/GUE edge universality in the supercritical sparsity regime, for symmetric/Hermitian rando…
We study a finite-horizon covariance steering problem for discrete-time Markov jump linear systems (MJLS) with both state- and control-dependent multiplicative noise. The objective is to minimize a qu…
Solutions to the Markov equation appear in many mathematical contexts. We aim to build on the understanding of them by proving a recent conjecture about Markov polynomials; solutions to a generalised …
This Part establishes the geometric theory of uniformly hyperbolic sets with explicit quantitative bounds throughout, and contains five main theorems. The Stable Manifold Theorem is proved via the bac…
Bangladesh exhibits marked year-to-year variability in dengue, partly driven by meteorological fluctuations that shape \textit{Aedes} breeding-site persistence, mosquito development, and transmission.…
A $k$-Markov number is a positive integer that appears in a positive integral solution to the Diophantine equation $x^2 + y^2 + z^2 + k(xy + xz + yz) = (3+3k)xyz$. This equation was introduced by Gyod…
We show that the Markov fractions introduced recently by Springborn coincide with the index of the Cohn matrices defined by Aigner. This provides a simple concatenation rule for the corresponding cont…
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