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DTSTART;TZID=America/New_York:20230906T160000
DTEND;TZID=America/New_York:20230906T170000
DTSTAMP:20240223T110729Z
CREATED:20240223T110729Z
LAST-MODIFIED:20240223T110729Z
UID:10002857-1694016000-1694019600@cmsa.fas.harvard.edu
SUMMARY:Light cones for open quantum systems
DESCRIPTION:Probability Seminar \nSpeaker: Marius Lemm\, University of Tuebingen \nTitle: Light cones for open quantum systems\n\nAbstract: We consider non-relativistic 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 finite-energy subspace. More precisely\, if the initial quantum state is localized in space\, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent 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 Lieb-Robinson bounds for lattice bosons. Based on joint works with S. Breteaux\, J. Faupin\, D.H. Ou Yang\, I.M. Sigal\, and J. Zhang.\n 
URL:https://cmsa.fas.harvard.edu/event/probability-9623/
LOCATION:Science Center 232\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.06.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230907T133000
DTEND;TZID=America/New_York:20230907T143000
DTSTAMP:20240223T110205Z
CREATED:20240223T110205Z
LAST-MODIFIED:20240223T110205Z
UID:10002855-1694093400-1694097000@cmsa.fas.harvard.edu
SUMMARY:Correlation decay for finite lattice gauge theories
DESCRIPTION:Probability Seminar \nSpeaker: Arka Adhikari (Stanford) \nTitle: Correlation decay for finite lattice gauge theories \nAbstract: In the setting of lattice gauge theories with finite (possibly non-Abelian) 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. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-9723/
LOCATION:Science Center 232\, Harvard Science Center\, 1 Oxford Street\, Cambridge MA 02138
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.07.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20230927T153000
DTEND;TZID=America/New_York:20230927T163000
DTSTAMP:20240223T112647Z
CREATED:20240223T112514Z
LAST-MODIFIED:20240223T112647Z
UID:10002862-1695828600-1695832200@cmsa.fas.harvard.edu
SUMMARY:Large deviations for the 3D dimer model
DESCRIPTION:Probability Seminar \nSpeaker: Catherine Wolfram (MIT) \nTitle: Large deviations for the 3D dimer model \nAbstract: 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 different from two\, explain how to formulate the large deviations principle in 3D\, show simulations\, and explain some of the ways that we use a smaller set of tools (e.g. Hall’s matching theorem or a double dimer swapping operation) in our arguments. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-92723/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.27.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231018T153000
DTEND;TZID=America/New_York:20231018T163000
DTSTAMP:20240223T075212Z
CREATED:20240223T075212Z
LAST-MODIFIED:20240223T075212Z
UID:10002829-1697643000-1697646600@cmsa.fas.harvard.edu
SUMMARY:Geometry of the doubly periodic Aztec dimer model
DESCRIPTION:Probability Seminar \nSpeaker: Tomas Berggren (MIT) \nTitle: Geometry of the doubly periodic Aztec dimer model \nAbstract: 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 and smooth regions and the number of cusps on the arctic curves. We will also discuss the convergence of local fluctuations to the appropriate translation-invariant Gibbs measures. Joint work with Alexei Borodin. \n  \n 
URL:https://cmsa.fas.harvard.edu/event/probability-101123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.18.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231025T153000
DTEND;TZID=America/New_York:20231025T163000
DTSTAMP:20240223T055719Z
CREATED:20240223T055628Z
LAST-MODIFIED:20240223T055719Z
UID:10002822-1698247800-1698251400@cmsa.fas.harvard.edu
SUMMARY:Tail estimates for stationary KPZ models
DESCRIPTION:Probability Seminar \nSpeaker: Benjamin Landon (University of Toronto) \nTitle: Tail estimates for stationary KPZ models \nAbstract: 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 non-integrable interacting diffusions. \nJoint work with Christian Noack and Phil Sosoe. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-102523/
LOCATION:Virtual
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-10.25.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231101T153000
DTEND;TZID=America/New_York:20231101T163000
DTSTAMP:20240223T054856Z
CREATED:20240223T054758Z
LAST-MODIFIED:20240223T054856Z
UID:10002821-1698852600-1698856200@cmsa.fas.harvard.edu
SUMMARY:Universality of max-margin classifiers
DESCRIPTION:Probability Seminar \nSpeaker: Youngtak Sohn (MIT) \nTitle: Universality of max-margin classifiers \nAbstract: 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 high-dimensional 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 max-margin classification\, has near-optimal prediction accuracy. Then\, we discuss universality of max-margin classification. In particular\, we characterize the prediction accuracy of the non-linear random features model\, a two-layer neural network with random first layer weights. The spectrum of the kernel random matrices plays a crucial role in the analysis. Finally\, we consider the wide-network limit\, where the number of neurons tends to infinity\, and show how non-linear max-margin classification with random features collapse to a linear classifier with a soft-margin objective. \nJoint work with Andrea Montanari\, Feng Ruan\, Jun Yan\, and Basil Saeed.
URL:https://cmsa.fas.harvard.edu/event/probability-11123/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.01.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231102T153000
DTEND;TZID=America/New_York:20231102T163000
DTSTAMP:20240223T113003Z
CREATED:20240223T113003Z
LAST-MODIFIED:20240223T113003Z
UID:10002865-1698939000-1698942600@cmsa.fas.harvard.edu
SUMMARY:Solving spin systems\, the Babylonian way
DESCRIPTION:Probability Seminar \nSpeaker: Nicola Kistler (Johann Wolfgang Goethe-Universität Frankfurt am Main) \nTitle: Solving spin systems\, the Babylonian way \nAbstract: 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 are still far from a clear understanding of the issues\, but quite astonishingly\, evidence is mounting that Parisi’s ultrametricity assumption\, the onset of scales and the universal hierarchical self-organisation of random systems in the infinite volume limit\, is intimately linked to hidden geometrical properties of large random matrices which satisfy rules reminiscent of the popular SUDOKU game.
URL:https://cmsa.fas.harvard.edu/event/probability-92023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-09.20.23.docx-1-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231108T153000
DTEND;TZID=America/New_York:20231108T163000
DTSTAMP:20240222T113941Z
CREATED:20240222T113928Z
LAST-MODIFIED:20240222T113941Z
UID:10002810-1699457400-1699461000@cmsa.fas.harvard.edu
SUMMARY:Fitting ellipsoids to random points
DESCRIPTION:Probability Seminar \nSpeaker: Antoine Maillard (ETH Zürich) \nTitle: Fitting ellipsoids to random points \nAbstract: 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: \n\nA proof that the problem is feasible for n < d^2 / C\, for some (large) constant C\, significantly improving over previously-known bounds.\nA non-rigorous characterization of the conjecture\, as well as significant generalizations\, using analytical methods of statistical physics.\nA rigorous proof of a satisfiability transition exactly at n = d^2 / 4 in a slightly relaxed version of the problem\, the first rigorous result characterizing the expected phase transition in ellipsoid fitting. The proof is inspired by the non-rigorous characterization discussed above.\n\nThis talk is based on the three manuscripts: arXiv:2307.01181\, arXiv:2310.01169\, arXiv:2310.05787\, which are joint works with A. Bandeira\, Tim Kunisky\, Shahar Mendelson and Elliot Paquette.
URL:https://cmsa.fas.harvard.edu/event/probability-11823/
LOCATION:Virtual
CATEGORIES:Probability Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231115T153000
DTEND;TZID=America/New_York:20231115T163000
DTSTAMP:20240223T054457Z
CREATED:20240223T053940Z
LAST-MODIFIED:20240223T054457Z
UID:10002818-1700062200-1700065800@cmsa.fas.harvard.edu
SUMMARY:Thresholds
DESCRIPTION:Probability Seminar \nSpeaker: Jinyoung Park (NYU) \nTitle: Thresholds \nAbstract: 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 p-biased 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 Gil Kalai conjectured that a natural (and often easy to calculate) lower bound q(F) (which we refer to as the “expectation-threshold”) for the threshold is in fact never far from its actual value. A positive answer to this conjecture enables one to narrow down the location of thresholds for any increasing properties in a tiny window. In particular\, this easily implies several previously very difficult results in probabilistic combinatorics such as thresholds for perfect hypergraph matchings (Johansson–Kahn–Vu) and bounded-degree spanning trees (Montgomery). I will present recent progress on this topic. Based on joint work with Keith Frankston\, Jeff Kahn\, Bhargav Narayanan\, and Huy Tuan Pham.
URL:https://cmsa.fas.harvard.edu/event/probability-111523/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.15.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231128T120000
DTEND;TZID=America/New_York:20231128T130000
DTSTAMP:20240222T113148Z
CREATED:20240222T113148Z
LAST-MODIFIED:20240222T113148Z
UID:10002809-1701172800-1701176400@cmsa.fas.harvard.edu
SUMMARY:A random matrix model towards the quantum chaos transition conjecture
DESCRIPTION:Probability Seminar \nSpeaker: Jun Yin (UCLA) \nTitle: A random matrix model towards the quantum chaos transition conjecture \nAbstract: 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. \nThis 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 the same phenomenon\, shedding light on the intricacies of this long-standing conjecture.
URL:https://cmsa.fas.harvard.edu/event/probability-112823/
LOCATION:MA
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Special-Seminar-11.28.23.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20231130T160000
DTEND;TZID=America/New_York:20231130T170000
DTSTAMP:20240223T052528Z
CREATED:20240223T052452Z
LAST-MODIFIED:20240223T052528Z
UID:10002815-1701360000-1701363600@cmsa.fas.harvard.edu
SUMMARY:A Gaussian convexity for logarithmic moment generating function
DESCRIPTION:Probability Seminar \nSpeaker: Wei-Kuo Chen (University of Minnesota) \nTitle: A Gaussian convexity for logarithmic moment generating function \nAbstract: 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 Paouris-Valettas small deviation inequality that arises from the study of convex geometry. The second provides a quantitative bound for the Dotsenko-Franz-Mezard conjecture in the Sherrington-Kirkpatrick mean-field spin glass model\, which states that the logarithmic anneal partition function of negative replica is asymptotically equal to the free energy. \n 
URL:https://cmsa.fas.harvard.edu/event/probability-113023/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Probability Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Probability-Seminar-11.30.23.png
END:VEVENT
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