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We consider the solution of the stochastic heat equation @TZ D 1 @ 2 X ZZ P W with delta function initial condition Z.T D0;X/ DiXD0 whose logarithm, with appropriate normalization, is the free energy… (More)

Macdonald processes are probability measures on sequences of partitions defined in terms of nonnegative specializations of the Macdonald symmetric functions and two Macdonald parameters $$q,t \in… (More)

We prove duality relations for two interacting particle systems: the $q$-deformed totally asymmetric simple exclusion process ($q$-TASEP) and the asymmetric simple exclusion process (ASEP).… (More)

- Ivan Corwin, A .E. Hammond
- 2011

Consider a collection of N Brownian bridges $B_{i}:[-N,N] \to \mathbb{R} $, Bi(−N)=Bi(N)=0, 1≤i≤N, conditioned not to intersect. The edge-scaling limit of this system is obtained by taking a weak… (More)

We consider two models for directed polymers in space-time independent random media (the O'Connell-Yor semidiscrete directed polymer and the continuum directed random polymer) at positive temperature… (More)

- Ivan Corwin
- 2015

We introduce an exactly-solvable model of random walk in random environment that we call the Beta RWRE. This is a random walk in $$\mathbb {Z}$$Z which performs nearest neighbour jumps with… (More)

We develop spectral theory for the generator of the q-Boson (stochastic) particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem has various… (More)

We introduce a four-parameter family of interacting particle systems on the line, which can be diagonalized explicitly via a complete set of Bethe ansatz eigenfunctions, and which enjoy certain… (More)

We consider the family of two-sided Bernoulli initial conditions for TASEP which, as the left and right densities (p-, ρ+) are varied, give rise to shock waves and rarefaction fans—the two phenomena… (More)