About

Ivan Corwin is a Professor in the Department of Mathematics at Columbia University. He earned his Ph.D. from the Courant Institute at New York University in 2011. His research focuses on Probability and Mathematical Physics.

Research topics

• Linguistics
• Philosophy

Selected publications

• Periodic Pitman Transforms and Jointly Invariant Measures

  Communications in Mathematical Physics · 2026-02-05

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• Periodic Pitman Transforms and Jointly Invariant Measures

  Communications in Mathematical Physics · 2026-02-05

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• Maximal free energy of the log-gamma polymer

  Journal d Analyse Mathématique · 2025-09-07

  articleOpen access
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• Universal KPZ Fluctuations for Moderate Deviations of Random Walks in Random Environments

  ArXiv.org · 2025-03-31

  preprintOpen access

  The theory of diffusion seeks to describe the motion of particles in a chaotic environment. Classical theory models individual particles as independent random walkers, effectively forgetting that particles evolve together in the same environment. Random Walks in a Random Environment (RWRE) models treat the environment as a random space-time field that biases the motion of particles based on where they are in the environment. We provide a universality result for the moderate deviations of the transition probability of this model over a wide class of choices of random environments. In particular, we show the convergence of moments to those of the multiplicative noise stochastic heat equation (SHE), whose logarithm is the Kardar-Parisi-Zhang (KPZ) equation. The environment only filters into the scaling limit through one parameter, which depends explicitly on the statistical description of the environment. This forms the basis for our introduction, in arXiv:2406.17733, of the extreme diffusion coefficient.

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• KPZ exponents for the half-space log-gamma polymer

  Probability Theory and Related Fields · 2024-10-10 · 5 citations

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• KPZ fixed point convergence of the ASEP and stochastic six-vertex models

  arXiv (Cornell University) · 2024-12-24

  preprintOpen access

  We consider the stochastic six-vertex (S6V) model and asymmetric simple exclusion process (ASEP) under general initial conditions which are bounded below lines of arbitrary slope at $\pm\infty$. We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that the height functions of these models converge to the KPZ fixed point. Previously, our results were known in the case of ASEP (for a particular direction in the rarefaction fan) via a comparison approach arXiv:2008.06584.

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• Stationary measures for integrable polymers on a strip

  Inventiones mathematicae · 2024-06-25 · 12 citations

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• Scaling limit of the colored ASEP and stochastic six-vertex models

  arXiv (Cornell University) · 2024-03-02 · 2 citations

  preprintOpen access

  We consider the colored asymmetric simple exclusion process (ASEP) and stochastic six vertex (S6V) model with fully packed initial conditions; the states of these models can be encoded by 2-parameter height functions. We show under Kardar-Parisi-Zhang (KPZ) scaling of time, space, and fluctuations that these height functions converge to the Airy sheet. Several corollaries follow. (1) For ASEP and the S6V model under the basic coupling, we consider the 4-parameter height function at position $y$ and time $t$ with a step initial condition at position $x$ and time $s < t$, and prove that under KPZ scaling it converges to the directed landscape. (2) We prove that ASEPs under the basic coupling, with multiple general initial data, converge to KPZ fixed points coupled through the directed landscape. (3) We prove that the colored ASEP stationary measures converge to the stationary horizon. (4) We prove a strong form of decoupling for the colored ASEP height functions, as well as for the stationary two-point function, as broadly predicted by the theory of non-linear fluctuating hydrodynamics. The starting point for our Airy sheet convergence result is an embedding of these colored models into a larger structure -- a color-indexed family of coupled line ensembles with an explicit Gibbs property, i.e., a colored Hall-Littlewood line ensemble. The core of our work then becomes to develop a framework to analyze the edge scaling limit of these ensembles.

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• Markov duality and Bethe ansatz formula for half-line open ASEP

  Probability and Mathematical Physics · 2024-01-30 · 7 citations

  articleOpen accessSenior author

  32 pages. v2: Minor edits and references added

  PublisherDOI

• Extreme Diffusion Measures Statistical Fluctuations of the Environment

  arXiv (Cornell University) · 2024-06-25

  preprintOpen access

  We consider many-particle diffusion in one spatial dimension modeled as Random Walks in a Random Environment (RWRE). A shared short-range space-time random environment determines the jump distributions that drive the motion of the particles. We determine universal power-laws for the environment's contribution to the variance of the extreme first passage time and extreme location. We show that the prefactors rely upon a single extreme diffusion coefficient that is equal to the ensemble variance of the local drift imposed on particles by the random environment. This coefficient should be contrasted with the Einstein diffusion coefficient, which determines the prefactor in the power-law describing the variance of a single diffusing particle and is equal to the jump variance in the ensemble averaged random environment. Thus a measurement of the behavior of extremes in many-particle diffusion yields an otherwise difficult to measure statistical property of the fluctuations of the generally hidden environment in which that diffusion occurs. We verify our theory and the universal behavior numerically over many RWRE models and system sizes.

  PublisherOA PDFDOI

Recent grants

• FRG: Collaborative Research: Integrable Probability

  NSF · $315k · 2017–2021

• Scaling Limits of Growth in Random Media

  NSF · $500k · 2018–2025

• Scaling limits of growth in random media

  NSF · $338k · 2023–2028

• Exact solvability of the Kardar-Parisi-Zhang stochastic partial differential equation

  NSF · $106k · 2014–2016

• Exact solvability of the Kardar-Parisi-Zhang stochastic partial differential equation

  NSF · $152k · 2012–2014

Frequent coauthors

• Alexei Borodin

  Massachusetts Institute of Technology

  97 shared

• Guillaume Barraquand

  Université Paris Cité

  57 shared

• Tomohiro Sasamoto

  27 shared

• Leonid Petrov

  University of Virginia

  25 shared

• Patrik L. Ferrari

  University of Bonn

  19 shared

• Alan Hammond

  19 shared

• Jeremy Quastel

  15 shared

• Li-Cheng Tsai

  14 shared

Education

• Ph.D., Probability and Mathematical Physics

  Courant Institute NYU

  2011