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Abstract
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We consider a Markov chain on nonnegative integer arrays of a given shape
(and satisfying certain constraints) which is closely related to fundamental
Whittaker functions and the Toda lattice. In the index zero case the arrays are
reverse plane partitions. We show that this Markov chain has nontrivial Markovian
projections and a unique entrance law starting from the array with all entries equal
to
.
We also discuss connections with imaginary exponential functionals
of Brownian motion, a semidiscrete polymer model with purely
imaginary disorder, interacting corner growth processes and discrete
-Bose
gas, extensions to other root systems, and hitting probabilities for some low rank
examples.
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Keywords
Whittaker functions, Toda lattice, reverse plane partitions
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Mathematical Subject Classification
Primary: 60J10, 60K35
Secondary: 05E05, 60B20, 82B23
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Milestones
Received: 14 December 2022
Revised: 31 August 2023
Accepted: 3 November 2023
Published: 29 November 2023
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© 2023 The Author(s), under
exclusive license to MSP (Mathematical Sciences
Publishers). |
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