Pfaffian Transition Probability and Correlation Kernel of TASEP in Half-space

2025/12/01 by Jan de Gier, W. R. Mead, de Gier, Jan +5
Mathematics · Physics and Astronomy · #Stochastic processes and statistical mechanics #Random Matrices and Applications #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2512.02286

Abstract

We present the transition probability for the asymmetric simple exclusion process on the half-space for general initial conditions and particle insertion at the boundary. In the limit of total asymmetry, where particles only jump to the right, we show that the transition probability reduces to a single Pfaffian for a large class of initial conditions. We further derive a Fredholm Pfaffian formula for the multipoint distribution of the totally asymmetric model conditioned on the number of particles in the system using a connection with a Pfaffian point process supported on Gelfand-Tsetlin patterns.

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