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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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A GUE central limit theorem and universality of directed first andlast passage site percolation
We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles…
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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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Combinatorics and Random Matrix Theory
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Random matrix central limit theorems for nonintersecting random walks
We consider nonintersecting random walks satisfying the condition that the increments have a finite moment generating function. We prove that in a certain limiting regime where the number of walks…
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A model for the bus system in Cuernavaca (Mexico)
TLDR
It is shown that introducing a natural repulsion does produce random matrix distributions in natural double scaling regimes and the circular bus model is introduced and introduced.
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Simple Systems with Anomalous Dissipation and Energy Cascade
We analyze a class of dynamical systems of the type $$\dot a_n(t) = c_{n-1} a_{n-1}(t) - c_n a_{n+1}(t) + f_n(t), n \epsilon {{\mathbb{N}}}, a_0=0,$$ where fn(t) is a forcing term with $$f_n(t)\not =…
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Convex minorants of random walks and Brownian motion
Let $(S_{i})_{i=0}^n$ be the random walk process generated by a sequence of real-valued independent identically distributed random variables $(X_{i})_{i=1}^n$ having densities. We study probability…
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A remark on a theorem of Chatterjee and last passage percolation
In this paper we prove universality of random matrix fluctuations of the last passage time of last passage percolation (LPP) in thin rectangles. The proof is a simple corollary of a theorem of…
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The Small Scales of the Stochastic Navier–Stokes Equations Under Rough Forcing
We prove that the small scale structures of the stochastically forced Navier–Stokes equations approach those of the naturally associated Ornstein–Uhlenbeck process as the scales get smaller.…
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