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We analyze the left-tail asymptotics of deformed Tracy-Widom distribution functions describing the fluctuations of the largest eigenvalue in invariant random matrix ensembles after removing each soft edge eigenvalue independently with…
We construct a probability model seemingly unrelated to the considered stochastic process of coagulation and fragmentation. By proving for this model the local limit theorem, we establish the asymptotic formula for the partition function of…
We deal with a random graph model evolving in discrete time steps by duplicating and deleting the edges of randomly chosen vertices. We prove the existence of an a.s. asymptotic degree distribution, with streched exponential decay; more…
In this paper, we present some asymptotic properties of the normalized inverse-Gaussian process. In particular, when the concentration parameter is large, we establish an analogue of the empirical functional central limit theorem, the…
These are notes from the lecture of Devavrat Shah given at the autumn school "Statistical Physics, Optimization, Inference, and Message-Passing Algorithms", that took place in Les Houches, France from Monday September 30th, 2013, till…
This is an expanded version of a series of lectures delivered by the second author in June, 2009. It describes the results of three of the authors' papers on ASEP, from the derivation of exact formulas for configuration probabilities,…
What is Statistics? Opinions vary. In fact, there is a continuous spectrum of attitudes toward statistics ranging from pure theoreticians, proving asymptotic efficiency and searching for most powerful tests, to wild practitioners, blindly…
This volume contains the joint proceedings of the Workshop on Games for the Synthesis of Complex Systems (CASSTING'16) and of the 3rd International Workshop on Synthesis of Complex Parameters (SynCoP'16). The workshops were held in…
These lecture notes grew out of notes for courses around Integrable PDEs and the KdV equation given by the authors during the past five years at the University of Antwerp (Belgium). Comments and suggestions are welcome.
We study averages of multiplicative eigenvalue statistics in ensembles of orthogonal Haar distributed matrices, which can alternatively be written as Toeplitz+Hankel determinants. We obtain new asymptotics for symbols with Fisher-Hartwig…
In the first part of the paper, we study the inversion statistic of random permutations under the family $(\mathbb{P}_\theta^{(n)})_{\theta \ge 0}$ of Ewens sampling distributions on $S_n$. We obtain a rather simple exact formula for the…
In this note we essentially simplify the proof of the main result in one paper from leading computer science conference 25th ACM Symposium on Parallelism in Algorithms and Architectures (see [3].) We also present direct method and give…
In 1986 J. Nuttall published in Constructive Approximation the paper "Asymptotics of generalized Jacobi polynomials", where with his usual insight he studied the behavior of the denominators ("generalized Jacobi polynomials") and the…
These notes are based on lectures delivered by G. Schehr at the XVIth School on Fundamental Problems in Statistical Physics (FPSP), held in Oropa (Italy) from 30 June to 11 July 2025. After a brief introduction to extreme value statistics…
In a recent paper, Bacher and de la Harpe study the conjugacy growth series of finitary permutation groups. In the course of studying the coefficients of a series related to the finitary alternating group, they introduce generalized…
These are lecture notes from a course offered at the Bangalore School on Statistical Physics - X, during 17-28 June 2019, [ https://www.icts.res.in/program/bssp2019 ] at International centre of theoretical physics (ICTS), Bangalore. These…
Lecture given Thursday 22 October 1992 at a Mathematics-Computer Science Colloquium at the University of New Mexico. The lecture was videotaped; this is an edited transcript.
This is a series of three lectures I gave at the Korea Institute of Advanced Study in June 2019 at a workshop about "Algebraic and Symplectic Aspects of Degenerations of Complex Surfaces". I focus on the symplectic aspects, in particular on…
GGR News: GGR Program at the APS meeting in Anaheim, CA by David Garfinkle We hear that..., by David Garfinkle 100 years ago, by David Garfinkle Research Briefs: Endpoint of the Gregory-Laflamme Instability, by Gary Horowitz Conference…
This volume of EPTCS contains the proceedings of the Sixth Workshop on Proof Exchange for Theorem Proving (PxTP 2019), held on 26 August 2019 as part of the CADE-27 conference in Natal, Brazil. The PxTP workshop series brings together…