Fermionic construction of tau functions and random processes

Abstract

Tau functions expressed as fermionic expectation values are shown to provide a natural and straightforward description of a number of random processes and statistical models involving hard core configurations of identical particles on the integer lattice, like a discrete version simple exclusion processes (ASEP), nonintersecting random walkers, lattice Coulomb gas models and others, as well as providing a powerful tool for combinatorial calculations involving paths between pairs of partitions. We study the decay of the initial step function within the discrete ASEP (d-ASEP) model as an example.

53 pages, 13 figures, a contribution to Proc. "Mathematics and Physics of Growing Interfaces"

References in corpus (8)

• Chaotic properties of systems with Markov dynamics
• Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
• Asymptotics of Plancherel-type random partitions
• Schur function expansion for normal matrix model and associated discrete matrix models
• Tau Functions and Matrix Integrals
• Janossy Densities I. Determinantal Ensembles
• Meixner polynomials and random partitions
• Virasoro action on Schur function expansions, skew Young tableaux and random walks

Cited by in corpus (8)

• Generation of Matrix Models by W-operators
• BGWM as Second Constituent of Complex Matrix Model
• Unitary Integrals and Related Matrix Models
• CKP Hierarchy, Bosonic Tau Function and Bosonization Formulae
• Symmetric polynomials, generalized Jacobi-Trudi identities and τ-functions
• Convolution symmetries of integrable hierarchies, matrix models and τ-functions
• Correlation function of the Schur process with a fixed final partition
• Aspects géométriques et intégrables des modèles de matrices aléatoires