
Speaker: WeiKuo ChenTitle: A Gaussian convexity for logarithmic moment generating functionVenue: CMSA Room G10Probability Seminar Speaker: WeiKuo Chen (University of Minnesota) Title: A Gaussian convexity for logarithmic moment generating function Abstract: Convex functions of Gaussian vectors are prominent objectives in many fields of mathematical studies. In this talk, I will establish a new convexity for the logarithmic moment generating function for this object and draw two consequences. The first leads to the PaourisValettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the DotsenkoFranzMezard conjecture in the SherringtonKirkpatrick meanfield spin glass model, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy. 

Speaker: Jun YinTitle: A random matrix model towards the quantum chaos transition conjectureVenue: Science Center 530Probability Seminar Speaker: Jun Yin (UCLA) Title: A random matrix model towards the quantum chaos transition conjecture Abstract: The Quantum Chaos Conjecture has long fascinated researchers, postulating a critical spectrum phase transition that separates integrable systems from chaotic systems in quantum mechanics. In the realm of integrable systems, eigenvectors remain localized, and local eigenvalue statistics follow the Poisson distribution. Conversely, chaotic systems exhibit delocalized eigenvectors, with local eigenvalue statistics mirroring the Sine kernel distribution, akin to the standard random matrix ensembles GOE/GUE. This talk delves into the heart of the Quantum Chaos Conjecture, presenting a novel approach through the lens of random matrix models. By utilizing these models, we aim to provide a clear and intuitive demonstration of… 

Speaker: Jinyoung ParkTitle: ThresholdsVenue: CMSA Room G10Probability Seminar Speaker: Jinyoung Park (NYU) Title: Thresholds Abstract: For a finite set X, a family F of subsets of X is said to be increasing if any set A that contains B in F is also in F. The pbiased product measure of F increases as p increases from 0 to 1, and often exhibits a drastic change around a specific value, which is called a “threshold.” Thresholds of increasing families have been of great historical interest and a central focus of the study of random discrete structures (e.g. random graphs and hypergraphs), with estimation of thresholds for specific properties the subject of some of the most challenging work in the area. In 2006, Jeff Kahn and… 

Speaker: Antoine MaillardTitle: Fitting ellipsoids to random pointsVenue: virtualProbability Seminar Speaker: Antoine Maillard (ETH Zürich) Title: Fitting ellipsoids to random points Abstract: We consider the problem of exactly fitting an ellipsoid (centered at 0) to n standard Gaussian random vectors in dimension d, for very large n and d. This problem has connections to questions in statistical learning and theoretical computer science, and is conjectured to undergo a sharp transition: with high probability, it has a solution if n < d^2/4, while it is not satisfiable if n > d^2/4. In this talk we will discuss the origin of this conjecture, and highlight some recent progress, in three different directions: A proof that the problem is feasible for n < d^2 / C, for some (large) constant… 

Speaker: Youngtak SohnTitle: Universality of maxmargin classifiersVenue: CMSA Room G10Probability Seminar Speaker: Youngtak Sohn (MIT) Title: Universality of maxmargin classifiers Abstract: Many modern learning methods, such as deep neural networks, are so complex that they perfectly fit the training data. Despite this, they generalize well to the unseen data. Motivated by this phenomenon, we consider highdimensional binary classification with linearly separable data. First, we consider Gaussian covariates and characterize linear classification problems for which the minimum norm interpolating prediction rule, namely the maxmargin classification, has nearoptimal prediction accuracy. Then, we discuss universality of maxmargin classification. In particular, we characterize the prediction accuracy of the nonlinear random features model, a twolayer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial… 

Speaker: Benjamin LandonTitle: Tail estimates for stationary KPZ modelsVenue: virtualProbability Seminar Speaker: Benjamin Landon (University of Toronto) Title: Tail estimates for stationary KPZ models Abstract: The limiting distributions of the KPZ universality class exhibit tail exponents of 3/2 and 3. In this talk we will review recent work studying the upper tail exponent 3/2 in the moderate deviations regime of several KPZ models at finite size, including the stochastic six vertex model, the ASEP and a class of nonintegrable interacting diffusions. Joint work with Christian Noack and Phil Sosoe. 

Speaker: Tomas BerggrenTitle: Geometry of the doubly periodic Aztec dimer modelVenue: CMSA Room G10Probability Seminar Speaker: Tomas Berggren (MIT) Title: Geometry of the doubly periodic Aztec dimer model Abstract: Random dimer models (or equivalently tiling models) have been a subject of extensive research in mathematics and physics for several decades. In this talk, we will discuss the doubly periodic Aztec diamond dimer model of growing size, with arbitrary periodicity and only mild conditions on the edge weights. In this limit, we see three types of macroscopic regions — known as rough, smooth and frozen regions. We will discuss how the geometry of the arctic curves, the boundary of these regions, can be described in terms of an associated amoeba and an action function. In particular, we determine the number of frozen… 

Speaker: Catherine WolframTitle: Large deviations for the 3D dimer modelVenue: CMSA Room G10Probability Seminar Speaker: Catherine Wolfram (MIT) Title: Large deviations for the 3D dimer model Abstract: A dimer tiling of Z^d is a collection of edges such that every vertex is covered exactly once. In 2000, Cohn, Kenyon, and Propp showed that 2D dimer tilings satisfy a large deviations principle. In joint work with Nishant Chandgotia and Scott Sheffield, we prove an analogous large deviations principle for dimers in 3D. A lot of the results for dimers in two dimensions use tools and exact formulas (e.g. the height function representation of a tiling or the Kasteleyn determinant formula) that are specific to dimension 2. In this talk, I will try to give some intuition for why three dimensions is… 

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… 

Speaker: Ron PeledTitle: Localization for random band matricesVenue: Harvard Science CenterProbability Seminar *Please note room change: Science Center 232* Speaker: Ron Peled (Tel Aviv University) Title: Localization for random band matrices Abstract: I will explain an approach via “an adaptive MerminWagner style shift” which proves localization of N x N Gaussian random band matrices with band width W satisfying W << N^{1/4}. Joint work with Giorgio Cipolloni, Jeffrey Schenker and Jacob Shapiro. 

Speaker: Ahmed El AlaouiTitle: Sampling from the SK and mixed pspin measures with stochastic localizationVenue: CMSA Room G10Probability Seminar Speaker: Ahmed El Alaoui (Cornell) Title: Sampling from the SK and mixed pspin measures with stochastic localization Abstract: I will present an algorithm which efficiently samples from the SherringtonKirkpatrick (SK) measure with no external field at high temperature. The approach is based on the stochastic localization process of Eldan, together with a subroutine for computing the mean vectors of a family of measures tilted by an appropriate external field. Conversely, we show that no ‘stable’ algorithm can approximately sample from the SK measure at low temperature. Time permitting, we discuss extensions to the pspin model. This is based on a joint work with Andrea Montanari and Mark Sellke. 

Speaker: WeiKuo ChenTitle: Some rigorous results on the Lévy spin glass modelVenue: virtualProbability Seminar Speaker: WeiKuo Chen (Minnesota) Title: Some rigorous results on the Lévy spin glass model Abstract: The Lévy spin glass model, proposed by CizeauBouchaud, is a meanfield model defined on a fully connected graph, where the spin interactions are formulated through a powerlaw distribution. This model is wellmotivated from the study of the experimental metallic spin glasses. It is also expected to bridge between some meanfield and diluted models. In this talk, we will discuss some recent progress on the Lévy model including its high temperature behavior and the existence and variational expression for the limiting free energy. Based on a joint work with Heejune Kim and Arnab Sen. 

Speaker: JeanChristophe MourratTitle: On the free energy of spin glasses with multiple typesVenue: virtualProbability Seminar Speaker: JeanChristophe Mourrat (ENS Lyon) Title: On the free energy of spin glasses with multiple types Abstract: In the simplest spinglass model, due to Sherrington and Kirkpatrick, the energy function involves interaction terms between all pairs of spins. A bipartite version of this model can be obtained by splitting the spins into two groups, which we can visualize as forming two layers, and by keeping only interaction terms that go from one to the other layer. For this and other models that incorporate a finite number of types of spins, the asymptotic behavior of the free energy remains mysterious (at least from the mathematical point of view). I will present the difficulties arising there, and some… 