概率论

We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the $L^p$-convergence of the marginal distributions towards the unique invariant measure for the…

We study a version of the classical Cayley-Moser optimal stopping problem, in which a seller must sell an asset by a given deadline, with the offers, which are independent random variables with a known distribution, arriving at random…

We analyze the general biased adjacent transposition shuffle process, which is a well-studied Markov chain on the symmetric group $S_n$. In each step, an adjacent pair of elements $i$ and $j$ are chosen, and then $i$ is placed ahead of $j$…

In this paper, we study favorite sites of one-dimensional asymmetric simple random walks. We show that almost surely, for any fixed integer $r\geq 1$, ``$r$ favorite sites" occurs infinitely often. We also give the asymptotic growth rate of…

We introduce a unified operator-theoretic framework for analyzing mixing times of finite-state ergodic Markov chains that applies to both reversible and non-reversible dynamics. The central object in our analysis is the projected transition…

This is the preface for the book by E. N. Dzhafarov, J. V. Kujala, and V. H. Cervantes, titled Contextuality in Random Variables: A Systematic Introduction. It is to be published by Cambridge University Press in 2026.

This paper studies a basic Markov chain, the Burnside process, on the space of flags $G/B$ with $G = GL_n(\mathbb{F}_q)$ and $B$ its upper triangular matrices. This gives rise to a shuffling: a Markov chain on the symmetric group realized…

We establish results on the conditional and standard convex order, as well as the increasing convex order, for two processes $ X = (X_t)_{t \in [0, T]} $ and $ Y = (Y_t)_{t \in [0, T]} $, defined by the following McKean-Vlasov equations…

In this paper, a method to exactly sample the trajectories of inverse subordinators (in the sense of the finite-dimensional distributions), jointly with the undershooting or overshooting process, is provided. The method applies to general…

The duality theory for monotone interacting particle systems was initiated by Gray (1986) and further developed by Sturm and Swart (2018). It contains the better known additive duality as a special case but differs in the sense that the…

We prove optimal convergence results of a stochastic particle method for computing the classical solution of a multivariate McKean-Vlasov equation, when the measure variable is in the drift, following the classical approach of [BT97,…

We study continuous mappings on the Heisenberg group that up to a time change preserve horizontal Brownian motion. It is proved that only harmonic morphisms possess this property.

Emerging applications of blockchains, such as grocery supply chains, require frequent updates to the data structure. This is in contrast with typical analyses of the Bitcoin blockchain, in which updates occur infrequently. With more…

We define censored fractional Bernstein derivatives on the positive half-line based on the Bernstein--Riemann--Liouville fractional derivative. The censored fractional derivative turns out to be the generator of the censored decreasing…

A large class of statistics can be formulated as smooth functions of sample means of random vectors. In this paper, we propose a general partial Cram\'{e}r's condition (GPCC) and apply it to establish the validity of the Edgeworth expansion…

In the present paper, we study the $(2,q)$-Ising-Potts model on the Cayley tree. We have derived a recurrence equation that shows the existence of a splitting Gibbs measure for this model. Furthermore, we have proven that for the…

In this paper, we study elastic Brownian motion on a \(C^2\) domain. Instead of being killed at the boundary, the process restarts from a random position inside the domain. We characterize this process through its stochastic differential…

We obtain a derivative formula for various notions of capacity. Namely we identify the second order term in the asymptotic expansion of the capacity of a union of two sets, as their distance goes to infinity. Our result applies to the usual…

In this paper, we examine applications of the theory of operator-valued processes to algebraic methods in probability theory. We show a central limit theorem for general conservation operator processes. Utilizing this, we analyze the…

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.…