3,380 research outputs found
Moduli spaces of d-connections and difference Painleve equations
We show that difference Painleve equations can be interpreted as isomorphisms
of moduli spaces of d-connections on the projective line with given singularity
structure. We also derive a new difference equation. It is the most general
difference Painleve equation known so far, and it degenerates to both
difference Painleve V and classical (differential) Painleve VI equations.Comment: 30 pages (LaTeX
Stochastic higher spin six vertex model and Macdonald measures
We prove an identity that relates the q-Laplace transform of the height function of a (higher spin inhomogeneous) stochastic six vertex model in a quadrant on one side and a multiplicative functional of a Macdonald measure on the other. The identity is used to prove the GUE Tracy-Widom asymptotics for two instances of the stochastic six vertex model via asymptotic analysis of the corresponding Schur measures.National Science Foundation (U.S.) (Grant DMS-1056390)National Science Foundation (U.S.) (Grant DMS-1607901
Generalized Green Functions and current correlations in the TASEP
We study correlation functions of the totally asymmetric simple exclusion
process (TASEP) in discrete time with backward sequential update. We prove a
determinantal formula for the generalized Green function which describes
transitions between positions of particles at different individual time
moments. In particular, the generalized Green function defines a probability
measure at staircase lines on the space-time plane. The marginals of this
measure are the TASEP correlation functions in the space-time region not
covered by the standard Green function approach. As an example, we calculate
the current correlation function that is the joint probability distribution of
times taken by selected particles to travel given distance. An asymptotic
analysis shows that current fluctuations converge to the process.Comment: 46 pages, 3 figure
A CLT for Plancherel representations of the infinite-dimensional unitary group
We study asymptotics of traces of (noncommutative) monomials formed by images
of certain elements of the universal enveloping algebra of the
infinite-dimensional unitary group in its Plancherel representations. We prove
that they converge to (commutative) moments of a Gaussian process that can be
viewed as a collection of simply yet nontrivially correlated two-dimensional
Gaussian Free Fields. The limiting process has previously arisen via the global
scaling limit of spectra for submatrices of Wigner Hermitian random matrices.
This note is an announcement, proofs will appear elsewhere.Comment: 12 page
Asymptotics of a discrete-time particle system near a reflecting boundary
We examine a discrete-time Markovian particle system on the quarter-plane
introduced by M. Defosseux. The vertical boundary acts as a reflecting wall.
The particle system lies in the Anisotropic Kardar-Parisi-Zhang with a wall
universality class. After projecting to a single horizontal level, we take the
longtime asymptotics and obtain the discrete Jacobi and symmetric Pearcey
kernels. This is achieved by showing that the particle system is identical to a
Markov chain arising from representations of the infinite-dimensional
orthogonal group. The fixed-time marginals of this Markov chain are known to be
determinantal point processes, allowing us to take the limit of the correlation
kernel.
We also give a simple example which shows that in the multi-level case, the
particle system and the Markov chain evolve differently.Comment: 16 pages, Version 2 improves the expositio
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