26 citations · 84 across the 17 of their papers we have counts for
18 papers
Periodic KPZ fixed point with general initial conditions
Jinho Baik, Yuchen Liao, Zhipeng Liu
We consider the relaxation-time-scale limit of the periodic totally asymmetric simple exclusion process (PTASEP) with general initial conditions. For every sequence of initial cond…
A conditional scaling limit of the KPZ fixed point with height tending to infinity at one location
Zhipeng Liu, Yizao Wang
We consider the asymptotic behavior of the KPZ fixed point conditioned on as goes to infinity. The main result is a…
When the geodesic becomes rigid in the directed landscape
Zhipeng Liu
When the value of the directed landscape at a point is sufficiently large, the geodesic from to is rigid and its location fl…
One-point distribution of the geodesic in directed last passage percolation
Zhipeng Liu
We consider the geodesic of the directed last passage percolation with iid exponential weights. We find the explicit one-point distribution of the geodesic location joint with the…
Limiting one-point distribution of periodic TASEP
Jinho Baik, Zhipeng Liu, Guilherme L. F. Silva
The relaxation time limit of the one-point distribution of the spatially periodic totally asymmetric simple exclusion process is expected to be the universal one point distribution…
Periodic TASEP with general initial conditions
Jinho Baik, Zhipeng Liu
We consider the one-dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain, and obtain explicit formulas for the…
Multi-point distribution of TASEP
Zhipeng Liu
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to a discrete TASEP model with step initi…
Integral formulas of ASEP and -TAZRP on a ring
Zhipeng Liu, Axel Saenz, Dong Wang
In this paper, we obtain the transition probability formulas for the Asymmetric Simple Exclusion Process (ASEP) and the -deformed Totally Asymmetric Zero Range Process (-TAZR…
Multi-point distribution of periodic TASEP
Jinho Baik, Zhipeng Liu
The height fluctuations of the models in the KPZ class are expected to converge to a universal process. The spatial process at equal time is known to converge to the Airy process o…
Malliavin-based Multilevel Monte Carlo Estimators for Densities of Max-stable Processes
Jose Blanchet, Zhipeng Liu
We introduce a class of unbiased Monte Carlo estimators for the multivariate density of max-stable fields generated by Gaussian processes. Our estimators take advantage of recent r…
Height fluctuations of stationary TASEP on a ring in relaxation time scale
Zhipeng Liu
We consider the totally asymmetric simple exclusion process on a ring with stationary initial conditions. The crossover between KPZ dynamics and equilibrium dynamics occurs when ti…
Exact Sampling of the Infinite Horizon Maximum of a Random Walk Over a Non-linear Boundary
Jose Blanchet, Jing Dong, Zhipeng Liu
We present the first algorithm that samples where is a mean zero random walk, and with defines a nonliner boundary. We show…
On Optimal Exact Simulation of Max-Stable and Related Random Fields
Zhipeng Liu, Jose H. Blanchet, A. B. Dieker +1
We consider the random field M(t)=\sup_{n\geq 1}\big\{-\log A_{n}+X_{n}(t)\big\}\,,\qquad t\in T\, for a set , where is an iid sequence of center…
TASEP on a ring in sub-relaxation time scale
Jinho Baik, Zhipeng Liu
Interacting particle systems in the KPZ universality class on a ring of size with number of particles are expected to change from KPZ dynamics to equilibrium dynamics at…
Fluctuations of TASEP on a ring in relaxation time scale
Jinho Baik, Zhipeng Liu
We consider the totally asymmetric simple exclusion process on a ring with flat and step initial conditions. We assume that the size of the ring and the number of particles tend to…
Fluctuations of TASEP and LPP with general initial data
Ivan Corwin, Zhipeng Liu, Dong Wang
We prove Airy process variational formulas for the one-point probability distribution of (discrete time parallel update) TASEP with general initial data, as well as last passage pe…
On the average of the Airy process and its time reversal
Jinho Baik, Zhipeng Liu
We show that the supremum of the average of the Airy process and its time reversal minus a parabola is distributed as the maximum of two independent GUE Tracy-Widom random variable…
Discrete Toeplitz/Hankel determinants and the width of non-intersecting processes
Jinho Baik, Zhipeng Liu
We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This ident…