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Random-walk in Beta-distributed random environment
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…
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Pfaffian Schur processes and last passage percolation in a half-quadrant
We study last passage percolation in a half-quadrant, which we analyze within the framework of Pfaffian Schur processes. For the model with exponential weights, we prove that the fluctuations of the…
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Facilitated exclusion process
We study the Facilitated TASEP, an interacting particle system on the one dimensional integer lattice. We prove that starting from step initial condition, the position of the rightmost particle has…
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HALF-SPACE MACDONALD PROCESSES
Macdonald processes are measures on sequences of integer partitions built using the Cauchy summation identity for Macdonald symmetric functions. These measures are a useful tool to uncover the…
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The $q$-Hahn asymmetric exclusion process
We introduce new integrable exclusion and zero-range processes on the one-dimensional lattice that generalize the $q$-Hahn TASEP and the $q$-Hahn Boson (zero-range) process introduced in [Pov13] and…
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A phase transition for q-TASEP with a few slower particles
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Large deviations for sticky Brownian motions
We consider n-point sticky Brownian motions: a family of n diffusions that evolve as independent Brownian motions when they are apart, and interact locally so that the set of coincidence times has…
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Moderate deviations for diffusion in time dependent random media
The position x(t) of a particle diffusing in a one-dimensional uncorrelated and time dependent random medium is simply Gaussian distributed in the typical direction, i.e. along the ray x = v 0 t,…
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Steady state of the KPZ equation on an interval and Liouville quantum mechanics
We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval with general Neumann-type boundary conditions and any…
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A short proof of a symmetry identity for the $q$-Hahn distribution
We give a short and elementary proof of a symmetry identity for the $q$-moments of the $q$-Hahn distribution arising in the study of the $q$-Hahn Boson process and the $q$-Hahn TASEP. This identity…
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