BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Asad Lodhia (University of Michigan) DTSTART:20200716T143000Z DTEND:20200716T153000Z DTSTAMP:20260422T225725Z UID:JIPS/1 DESCRIPTION:Title: Mat rix Means and a Novel High-dimensional Shrinkage Phenomenon\nby Asad L odhia (University of Michigan) as part of Junior Integrable Probability Se minar\n\n\nAbstract\nWe analyze the impact on covariance estimation of tak ing a Harmonic mean as opposed to an arithmetic mean of a collection of Wi shart Random Matrices in high dimensions. We see that the Harmonic mean im proves on the operator norm estimation but curiously does not improve eige nvector recovery as suggested by the Davis-Kahan Inequality. Based on join t work with E. Levina and K. Levin\n LOCATION:https://researchseminars.org/talk/JIPS/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Yier Lin (Columbia University) DTSTART:20200806T143000Z DTEND:20200806T153000Z DTSTAMP:20260422T225725Z UID:JIPS/2 DESCRIPTION:Title: Lya punov exponents of the SHE for general initial data\nby Yier Lin (Colu mbia University) as part of Junior Integrable Probability Seminar\n\n\nAbs tract\nWe consider the 1+1 dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Paris i-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exp onents of the SHE for a large class of initial data which includes any bou nded deterministic positive initial data and the stationary initial data. As a consequence\, we derive exact formulas for the upper tail large devia tion rate functions of the KPZ equation for general initial data. Joint wo rk with Promit Ghosal.\n\nGo to https://sites.google.com/view/junior-ips f or zoom link and password.\n LOCATION:https://researchseminars.org/talk/JIPS/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Ofer Busani (University of Bristol) DTSTART:20200813T160000Z DTEND:20200813T170000Z DTSTAMP:20260422T225725Z UID:JIPS/3 DESCRIPTION:Title: Uni versality of geodesic tree in last passage percolation\nby Ofer Busani (University of Bristol) as part of Junior Integrable Probability Seminar\ n\n\nAbstract\nIn Last Passage Percolation (LPP) one assumes i.i.d. weight s on the lattice Z^2. The geodesic from the anti-diagonal h(x)=-x to the p oint (N\,N) is an up-right path starting from h and terminating at (N\,N) on which the total weight is maximal. Consider now a cylinder H of width εN^2/3 and length ε^{3/2-}N centered around the point (N\,N) and along t he straight line going from the point (0\,0) to the point (N\,N). The geod esic tree consists of all the geodesics going from h and terminating in th e cylinder H. We show that for exponential LPP\, for a large class of weig hts on h(x) and with high probability\, the geodesic tree coincides on H w ith a universal stationary tree.\n LOCATION:https://researchseminars.org/talk/JIPS/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jimmy He (Stanford University) DTSTART:20200821T000000Z DTEND:20200821T010000Z DTSTAMP:20260422T225725Z UID:JIPS/4 DESCRIPTION:Title: Lim it theorems for descents of Mallows permutations\nby Jimmy He (Stanfor d University) as part of Junior Integrable Probability Seminar\n\n\nAbstra ct\nThe Mallows measure on the symmetric group gives a way to generate ran dom permutations which are more likely to be sorted than not. There has be en a lot of recent work to try and understand the limiting properties of M allows permutations. I'll discuss recent work on the joint distribution of descents\, a statistic counting the number of "drops" in a permutation\, and descents in its inverse\, generalizing work of Chatterjee and Diaconis \, and Vatutin. The proof is new even in the uniform case and uses Stein's method with a size-bias coupling as well as a regenerative representation of Mallows permutations.\n LOCATION:https://researchseminars.org/talk/JIPS/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Guilherme Silva (Universidade de São Paulo) DTSTART:20200903T140000Z DTEND:20200903T150000Z DTSTAMP:20260422T225725Z UID:JIPS/5 DESCRIPTION:Title: Per iodic TASEP: when integrable systems meet integrable probability (once aga in)\nby Guilherme Silva (Universidade de São Paulo) as part of Junior Integrable Probability Seminar\n\n\nAbstract\nIt is well-known that the T racy-Widom distributions admit representations involving solutions to part icular integrable systems. Other marginals of the KPZ fixed point\, such a s the Airy2 process\, also admit similar representations. And very recentl y\, first by Quastel and Remenik and shortly afterwards by Le Doussal\, st atistics of the KPZ fixed point were found to be connected to the KP equat ion.\n\nIn this talk\, we plan to overview some analogue connections\, but now for distributions of the periodic TASEP (pTASEP)\, which are believed to be the universal analogue of the KPZ universality class for periodic s etup. For the step periodic initial condition\, we compare the limiting on e-point distribution of the pTASEP with the GUE Tracy-Widom distribution\, highlighting the key features that allow to connect both of them to coupl ed systems of mKdV and heat equations. We also discuss some asymptotic pro perties of this limiting distribution\, showing that it interpolates betwe en the GUE Tracy-Widom and a Gaussian. For pTASEP with general initial con dition\, we also explain how very few analytic aspects of its limiting one -point distribution give a connection with the KP equation\, in analogous way to Quastel-Remenik’s mentioned result. This talk is based on joint w ork with Jinho Baik (University of Michigan) and Zhipeng Liu (University o f Kansas). Time permitting\, we also briefly discuss a work in progress wi th Jinho Baik and Andrei Prokhorov (University of Michigan)\, greatly exte nding the mentioned results to multipoint distributions.\n LOCATION:https://researchseminars.org/talk/JIPS/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Sung-Soo Byun (Seoul National University) DTSTART:20200910T140000Z DTEND:20200910T150000Z DTSTAMP:20260422T225725Z UID:JIPS/6 DESCRIPTION:Title: A n on-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality\nby Sung-Soo Byun (Seoul National U niversity) as part of Junior Integrable Probability Seminar\n\n\nAbstract\ nIn this talk\, I will discuss complex eigenvalues of the product of two r ectangular complex Ginibre matrices that are correlated through a non-Herm iticity parameter.\n\nIn the first half\, I will present the limiting spec tral distribution of the model\, which interpolates between classical resu lts for random matrices on the global scale\, the circular law and the Mar chenko-Pastur distribution. In the second half\, I will explain the micros copic behaviours of the model\, which includes the limiting local correlat ion kernel at multi-criticality\, where the interior of the spectrum split s into two connected components.\n\nThe global statistics follows from the solution of certain equilibrium measure problem and concentration for the 2D Coulomb gases on Frostman’s equilibrium measure\, whereas the local statistics follows from a saddle point analysis of the kernel of orthogona l Laguerre polynomials in the complex plane.\n\nThis is based on joint wor k with Gernot Akemann and Nam-Gyu Kang.\n LOCATION:https://researchseminars.org/talk/JIPS/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Andrew Ahn (Columbia University) DTSTART:20200925T160000Z DTEND:20200925T170000Z DTSTAMP:20260422T225725Z UID:JIPS/7 DESCRIPTION:Title: Add ition of Random Matrices and Quantized Analogues\nby Andrew Ahn (Colum bia University) as part of Junior Integrable Probability Seminar\n\n\nAbst ract\nThe main objects of this talk are particle processes coming from the eigenvalues of sums of unitarily invariant random matrices and quantized analogues which arise from tensor products of irreducible representations of the unitary group. We outline an integrable probability approach to obt aining Airy point process fluctuations at the edge under an asymptotic reg ime where the number of summands or tensor products is sufficiently large. \n LOCATION:https://researchseminars.org/talk/JIPS/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Dominik Schmid (TU Munich) DTSTART:20201009T140000Z DTEND:20201009T150000Z DTSTAMP:20260422T225725Z UID:JIPS/8 DESCRIPTION:Title: The TASEP on trees\nby Dominik Schmid (TU Munich) as part of Junior Integ rable Probability Seminar\n\n\nAbstract\nWe study the totally asymmetric s imple exclusion process (TASEP) on rooted trees. This means that particles are generated at the root and can only jump in the direction away from th e root under the exclusion constraint. Our interests are two-fold. On the one hand\, we study invariant measures for the TASEP on trees and provide sufficient conditions for the existence of non-trivial equilibrium distrib utions. On the other hand\, we consider the evolution of the TASEP on tree s when all sites are initially empty and study currents.\n\nThis talk is b ased on joint work with Nina Gantert and Nicos Georgiou.\n LOCATION:https://researchseminars.org/talk/JIPS/8/ END:VEVENT END:VCALENDAR