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Fluctuations of TASEP and LPP with general initial data
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 percolation from a…
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Multipoint distribution of periodic TASEP
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 or its variations.…
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Fluctuations of TASEP on a Ring in Relaxation Time Scale
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 infinity…
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Discrete Toeplitz/Hankel Determinants and the Width of Nonintersecting Processes
We show that the ratio of a discrete Toeplitz/Hankel determinant and its continuous counterpart equals a Freholm determinant involving continuous orthogonal polynomials. This identity is used to…
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On logarithmically optimal exact simulation of max-stable and related random fields on a compact set
Published in: Bernoulli DOI: 10.3150/18-BEJ1076 Publication date: 2019 Document version Peer reviewed version Document license: Other Citation for published version (APA): Liu, Z., Blanchet, J. H.,…
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TASEP on a Ring in Sub-relaxation Time Scale
Interacting particle systems in the KPZ universality class on a ring of size L with O(L) number of particles are expected to change from KPZ dynamics to equilibrium dynamics at the so-called…
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Periodic TASEP with general initial conditions
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…
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Multi-time distribution of TASEP
Recently Johansson and Rahman obtained the limiting multi-time distribution for the discrete polynuclear growth model, which is equivalent to discrete TASEP model with step initial condition. In this…
On Optimal Exact Simulation of Max-Stable and Related Random Fields
TLDR
The random field M(t) is considered, for a set $T\subset \mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0 0$ with complexity $o(c(d)\,d^{\epsilon })$, where $M$ can be a.s. converging series representation.
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Height fluctuations of stationary TASEP on a ring in relaxation time scale
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 time is proportional…
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