## Integrable Probability and Related Fields from a Safe Distance

**Seminar description:**Talks should ideally highlight a key idea or technique which is interesting and comprehensible to those on other parts of the field, and we especially welcome talks which are largely or entirely expository.

**Schedule:**

**Previous talks:**

*Global asymptotics of particle systems at high temperature.*(slides)

Title: *Lozenge tilings and the Gaussian free field on a cylinder. *(slides/video)

Abstract: In this talk I will first give an expository survey of some of what is known and conjectured about limit shapes and Gaussian free field fluctuations for height functions of random lozenge tilings. I will then discuss new results on lozenge tilings on an infinite cylinder, which may be analyzed using the periodic Schur process introduced by Borodin, and which exhibit interesting behaviors not present for tilings of simply connected domains. Under one variant of the $q^{vol}$ measure, corresponding to random cylindric partitions, the height function converges to a deterministic limit shape and fluctuations around it are given by the Gaussian free field in the conformal structure predicted by the Kenyon-Okounkov conjecture. Under another variant, corresponding to an unrestricted tiling model on the cylinder, the fluctuations are given by the same Gaussian free field with an additional discrete Gaussian shift component. Fluctuations of the latter type have been previously conjectured by Gorin for tiling models on planar domains with holes. This is joint work with Andrew Ahn and Marianna Russkikh.

**(Wednesday)**Speaker: Yaroslav Kubivskyi (University of Geneva)

**11/27/2020. Friday, 3pm**

*Schramm Loewner Evolution.*

**10:00 am.**

*Sums and products of invariant ensembles.*

**2:30pm.**

**Joint seminar with Columbia University.**

*Multivariate normal approximation for traces of random unitary matrices.*

*Coalescence estimates for the corner growth model with exponential weights.*

*Ising model on random triangulations of the half-plane: critical behavior and phase transition.*

*Short time large deviations of the KPZ equation.*

*We establish the Freidlin--Wentzell Large Deviation Principle (LDP) for the Stochastic Heat Equation with multiplicative noise in one spatial dimension. That is, we introduce a small parameter $\sqrt{\epsilon}$ to the noise, and establish an LDP for the trajectory of the solution. Such a Freidlin--Wentzell LDP gives the short-time, one-point LDP for the KPZ equation in terms of a variational problem. Analyzing this variational problem under the narrow wedge initial data, we prove a quadratic law for the near center tail and a 5/2 law for the deep lower tail. These power laws confirm existing physics predictions Kolokolov and Korshunov (2007), Kolokolov and Korshunov (2009), Meerson, Katzav, and Vilenkin (2016), Le Doussal, Majumdar, Rosso, and Schehr (2016), and Kamenev, Meerson, and Sasorov (2016). Joint work with Li-Cheng Tsai.*

*Multi-phase z-measures and their origins.*

*Exponential Decay of Correlations in the two dimensional Random Field Ising Model.*

*Matrix Product Ansatz and ASEP.*

*Probabilistic Liouville conformal blocks and its properties*.

*Arctic Boundaries in Ice Models*.

*The Airy Sheet and the directed landscape*.

*Part II.*

*The Airy Sheet and the directed landscape*.

*Part I.*

*On topological correlations in planar Ashkin-Teller models*.

*The eight-vertex model via dimers*.

**6:00pm**Speaker: Matteo Mucciconi (Tokyo Institute of Technology)

*Stochastic vertex models and interlacing arrays*.

*Kerov's mixing construction and the representation ring of finite groups*

*ASEP through symmetric functions*.

^{1/3}fluctuations of the height function. I will discuss the proof of Borodin and Olshanski of some of these results, which are based on symmetric functions machinery. I will also discuss how their results can be applied to ASEP with finitely many particles.

*The beta random walk in random environment.*

*Yang-Baxter equation and symmetric functions.*

*Probabilistic Aspects of the KPZ equation.*

*Smirnov's proof of Cardy's formula and around.*

*Stochastic 6-vertex model in integrable probability.*

*Symmetric functions and random matrices.*

*GFF in q*

^{vol}plane partitions.*Discrete complex analysis in lattice models. Part II.*

*Discrete complex analysis in lattice models. Part I.*