During the 2023–24 academic year, the CMSA will be hosting a Probability Seminar organized by Benjamin McKenna, Changji Xu, and Kevin Yang. This seminar will take place on Wednesdays from 3:30–4:30 pm (Eastern Time) in Room G10 at the CMSA, 20 Garden Street, Cambridge MA 02138. Some meetings will take place virtually on Zoom or be held in hybrid formats. The schedule will be updated as talks are confirmed. To join the Probability Seminar Listserv, please visit this LINK.

  • December 13, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • December 06, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • November 29, 2023 03:30 PM
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Venue: CMSA Room G10

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  • November 22, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • November 15, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • November 08, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • November 01, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • October 25, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • October 18, 2023 03:30 PM
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Venue: CMSA Room G10

Probability Seminar  

  • October 11, 2023 03:30 PM
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  • October 04, 2023 03:30 PM
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Probability Seminar  

  • September 27, 2023 03:30 PM
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Probability Seminar  

  • September 20, 2023 03:30 PM
Speaker: Nicola Kistler
Title: Solving spin systems, the Babylonian way
Venue: CMSA Room G10

Probability Seminar Speaker: Nicola Kistler (Johann Wolfgang Goethe-Universität 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…

  • September 07, 2023 01:30 PM
Speaker: Arka Adhikari
Title: Correlation decay for finite lattice gauge theories
Venue: Science Center 232

Probability Seminar Speaker: Arka Adhikari (Stanford) Title: Correlation decay for finite lattice gauge theories Abstract: 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.  

  • September 06, 2023 04:00 PM
Speaker: Marius Lemm
Title: Light cones for open quantum systems
Venue: Science Center 232

Probability Seminar Speaker: Marius Lemm, University of Tuebingen Title: Light cones for open quantum systems Abstract: 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…

  • May 11, 2023 01:30 PM
Speaker: Giorgio Cipolloni
Title: How do the eigenvalues of a large non-Hermitian random matrix behave?
Venue: Harvard Science Center

Probability Seminar Speaker: Giorgio Cipolloni (Princeton) Title: How do the eigenvalues of a large non-Hermitian 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 non-natural 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

  • May 03, 2023 03:30 PM
Speaker: Boris Hanin
Title: Random Neural Networks
Venue: CMSA Room G10

Probability 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…

  • April 26, 2023 03:30 PM
Speaker: Jimmy He
Title: Boundary current fluctuations for the half space ASEP
Venue: CMSA Room G10

Probability 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 Baik-Rains 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 Hall-Littlewood process, and the free boundary Schur process, which allows exact formulas to be computed.

  • April 19, 2023 03:30 PM
Speaker: Evita Nestoridi
Title: Diagonalizing Transition Matrices of Card Shuffles
Venue: Science Center 232

Probability 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 random-to-random card shuffle. In this talk we will discuss connections between these techniques as well as application to card shuffling.

  • April 12, 2023 03:30 PM
Speaker: Emma Bailey
Title: Large deviations of Selberg’s central limit theorem
Venue: CMSA Room G10

Probability 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…