












Speaker: Nicola KistlerTitle: Solving spin systems, the Babylonian wayVenue: CMSA Room G10Probability Seminar Speaker: Nicola Kistler (Johann Wolfgang GoetheUniversität Frankfurt am Main) Title: Solving spin systems, the Babylonian way Abstract: The replica method, together with Parisi’s symmetry breaking mechanism, is an extremely powerful tool to compute the limiting free energy of virtually any mean field disordered system. Unfortunately, the tool is dramatically flawed from a mathematical point of view. I will discuss a truly elementary procedure which allows to rigorously implement two (out of three) steps of the replica method, and conclude with some remarks on the relation between this new point of view and old work by Mezard and Virasoro on the microstructure of ultrametricity, the latter being the fundamental yet unjustified Ansatz in the celebrated Parisi solution. We… 

Speaker: Arka AdhikariTitle: Correlation decay for finite lattice gauge theoriesVenue: Science Center 232Probability Seminar Speaker: Arka Adhikari (Stanford) Title: Correlation decay for finite lattice gauge theories Abstract: In the setting of lattice gauge theories with finite (possibly nonAbelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao. 

Speaker: Marius LemmTitle: Light cones for open quantum systemsVenue: Science Center 232Probability Seminar Speaker: Marius Lemm, University of Tuebingen Title: Light cones for open quantum systems Abstract: We consider nonrelativistic Markovian open quantum dynamics in continuous space. We show that, up to small probability tails, the supports of quantum states propagate with finite speed in any finiteenergy subspace. More precisely, if the initial quantum state is localized in space, then any finiteenergy part of the solution of the von NeumannLindblad equation is approximately localized inside an energydependent light cone. We also obtain an explicit upper bound on the slope of this light cone (i.e., on the maximal speed). The general method can be used to derive propagation bounds for a variety of other quantum systems including LiebRobinson bounds for lattice… 

Speaker: Giorgio CipolloniTitle: How do the eigenvalues of a large nonHermitian random matrix behave?Venue: Harvard Science CenterProbability Seminar Speaker: Giorgio Cipolloni (Princeton) Title: How do the eigenvalues of a large nonHermitian random matrix behave? Abstract: We prove that the fluctuations of the eigenvalues converge to the Gaussian Free Field (GFF) on the unit disk. These fluctuations appear on a nonnatural scale, due to strong correlations between the eigenvalues. Then, motivated by the long time behaviour of the ODE \dot{u}=Xu, we give a precise estimate on the eigenvalue with the largest real part and on the spectral radius of X. Location: Science Center Room 232 

Speaker: Boris HaninTitle: Random Neural NetworksVenue: CMSA Room G10Probability Seminar Speaker: Boris Hanin (Princeton) Title: Random Neural Networks Abstract: Fully connected neural networks are described two by structural parameters: a depth L and a width N. In this talk, I will present results and open questions about the asymptotic analysis of such networks with random weights and biases in the regime where N (and potentially L) are large. The first set of results are for deep linear networks, which are simply products of L random matrices of size N x N. I’ll explain how the setting where the ratio L / N is fixed with both N and L large reveals a number of phenomena not present when only one of them is large. I will then state… 

Speaker: Jimmy HeTitle: Boundary current fluctuations for the half space ASEPVenue: CMSA Room G10Probability Seminar Speaker: Jimmy He (MIT) Title: Boundary current fluctuations for the half space ASEP Abstract: The half space asymmetric simple exclusion process (ASEP) is an interacting particle system on the half line, with particles allowed to enter/exit at the boundary. I will discuss recent work on understanding fluctuations for the number of particles in the half space ASEP started with no particles, which exhibits the BaikRains phase transition between GSE, GOE, and Gaussian fluctuations as the boundary rates vary. As part of the proof, we find new distributional identities relating this system to two other models, the half space HallLittlewood process, and the free boundary Schur process, which allows exact formulas to be computed. 

Speaker: Evita NestoridiTitle: Diagonalizing Transition Matrices of Card ShufflesVenue: Science Center 232Probability Seminar Speaker: Evita Nestoridi (Stonybrook) Title: Diagonalizing Transition Matrices of Card Shuffles Abstract: In their seminal work, Diaconis and Shahshahani used representation theory of the symmetric group to diagonalize the transition matrix of random transpositions. More recently, Dieker and Saliola introduced another technique to diagonalize the randomtorandom card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling. 

Speaker: Emma BaileyTitle: Large deviations of Selberg’s central limit theoremVenue: CMSA Room G10Probability Seminar Speaker: Emma Bailey (CUNY) Title: Large deviations of Selberg’s central limit theorem Abstract: Selberg’s CLT concerns the typical behaviour of the Riemann zeta function and shows that the random variable $\Re \log \zeta(1/2 + i t)$, for a uniformly drawn $t$, behaves as a Gaussian random variable with a particular variance. It is natural to investigate how far into the tails this Gaussianity persists, which is the topic of this work. There are also very close connections to similar problems in circular unitary ensemble characteristic polynomials. It transpires that a `multiscale scheme’ can be applied to both situations to understand these questions of large deviations, as well as certain maxima and moments. In this talk I… 