44 citations · 187 across the 43 of their papers we have counts for
24 papers · 1 filter
The occupation time of a random walk generated by the uniform random permutation--a GPT-6 Astra proof
Wenpin Tang
This note provide a proof of Conjecture 2.5 in Fang et al. (J. Appl. Probab., 58(4):851--867, 2021), with the help of \texttt{GPT-6 Astra}. We show that the number of edges lying a…
Systemic robustness: a mean-field particle system approach
Erhan Bayraktar, Gaoyue Guo, Wenpin Tang +1
This paper is concerned with the problem of budget control in a large particle system modeled by stochastic differential equations involving hitting times, which arises from consid…
Hidden symmetries and limit laws in the extreme order statistics of the Laplace random walk
Jim Pitman, Wenpin Tang
This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the…
Simulated annealing from continuum to discretization: a convergence analysis via the Eyring--Kramers law
Wenpin Tang, Xun Yu Zhou
We study the convergence rate of continuous-time simulated annealing and its discretization for approximating the global optimum of a…
McKean-Vlasov equations involving hitting times: blow-ups and global solvability
Erhan Bayraktar, Gaoyue Guo, Wenpin Tang +1
This paper is concerned with the analysis of blow-ups for two McKean-Vlasov equations involving hitting times. Let be standard Brownian motion, and $τ:= \inf\{…
Extreme order statistics of random walks
Jim Pitman, Wenpin Tang
This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum…
Arcsine laws for random walks generated from random permutations with applications to genomics
Xiao Fang, Han Liang Gan, Susan Holmes +4
A classical result for the simple symmetric random walk with steps is that the number of steps above the origin, the time of the last visit to the origin, and the time of the…
The Poisson binomial distribution -- Old & New
Wenpin Tang, Fengmin Tang
This is an expository article on the Poisson binomial distribution. We review lesser known results and recent progress on this topic, including geometry of polynomials and distribu…
Ergodicity of the infinite swapping algorithm at low temperature
Georg Menz, André Schlichting, Wenpin Tang +1
Sampling Gibbs measures at low temperatures is an important task but computationally challenging. Numerical evidence suggests that the infinite-swapping algorithm (isa) is a promis…
Exponential ergodicity and convergence for generalized reflected Brownian motion
Wenpin Tang
In this paper we provide convergence analysis for a class of Brownian queues in tandem by establishing an exponential drift condition. A consequence is the uniform exponential ergo…
One-dependent colorings of the star graph
Thomas M. Liggett, Wenpin Tang
This paper is concerned with symmetric -dependent colorings of the -ray star graph for . We compute the critical point of the -dependent hard-core…
Renewal sequences and record chains related to multiple zeta sums
Jean-Jil Duchamps, Jim Pitman, Wenpin Tang
For the random interval partition of generated by the uniform stick-breaking scheme known as GEM, let be the probability that the first intervals created by…
Regenerative random permutations of integers
Jim Pitman, Wenpin Tang
Motivated by recent studies of large Mallows permutations, we propose a class of random permutations of and of , called regenerative permutations.…
The argmin process of random walks and Lévy processes
Jim Pitman, Wenpin Tang
In this paper we consider the argmin process of random walks and Lévy processes. We prove that they enjoy the Markov property, and provide their transition kernels in some special…
The argmin process of random walks, Brownian motion and Lévy processes
Jim Pitman, Wenpin Tang
In this paper we investigate the argmin process of Brownian motion defined by for . The argm…
Transporting random measures on the line and embedding excursions into Brownian motion
Günter Last, Wenpin Tang, Hermann Thorisson
We consider two jointly stationary and ergodic random measures and on the real line with equal intensities. An allocation is an equivariant random mapping from…
Tree formulas, mean first passage times and Kemeny's constant of a Markov chain
Jim Pitman, Wenpin Tang
In this paper, we aim to provide probabilistic and combinatorial insights into tree formulas for the Green function and hitting probabilities of Markov chains on a finite state spa…
Optimal Surviving Strategy for Drifted Brownian Motions with Absorption
Wenpin Tang, Li-Cheng Tsai
We study the 'Up the River' problem formulated by Aldous (2002), where a unit drift is distributed among a finite collection of Brownian particles on , which are an…
The spans in Brownian motion
Steven N. Evans, Jim Pitman, Wenpin Tang
For , let be a -dimensional standard Brownian motion. We study the -Brownian span set $Span(d):=\{t-s;~ B^d_s=B^d_t~\mbox{for some}~0 \l…
Patterns in random walks and Brownian motion
Jim Pitman, Wenpin Tang
We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptot…
The Slepian zero set, and Brownian bridge embedded in Brownian motion by a spacetime shift
Jim Pitman, Wenpin Tang
This paper is concerned with various aspects of the Slepian process derived from a one-dimensional Brownian motion . In particular, we o…
A note on the frontier of a branching reflected Brownian motion
Wenpin Tang
In this note, we study the asymptotical frontier behavior of a branching reflected Brownian motion. There is essentially no difference in maximal displacement between a branching B…
The Vervaat transform of Brownian bridges and Brownian motion
Titus Lupu, Jim Pitman, Wenpin Tang
For a continuous function , define the Vervaat transform , where corresponds to the fir…
On Vervaat transform of Brownian bridges and Brownian motion
Jim Pitman, Wenpin Tang
For a continuous function , define the Vervaat transform , where corresponds to the fir…