Schedule

• Jan 21
  Tuesday, 1:30-2:30pm, 2-449

  Philip Easo (Caltech)

  Cutsets and percolation

  Abstract: The classical Peierls argument establishes that percolation on a graph G has a non-trivial (uniformly) percolating phase if G has “not too many small cutsets”. Severo, Tassion, and I have recently proved the converse. Our argument is inspired by an idea from computer science and fits on one page. Our new approach also resolves a conjecture of Babson of Benjamini from 1999 and provides a much simpler proof of the celebrated result of Duminil-Copin, Goswami, Raoufi, Severo, and Yadin that percolation on any transitive graph with superlinear growth undergoes a non-trivial phase transition.

• Feb 3

  Yi Han (MIT)

  Some progress and mysteries in the study of inhomogeneous random matrices

  Abstract: The spectrum of a random matrix is well-understood for an invariant ensemble, and sufficiently strong information has been obtained for mean field type random matrices. There are however far more general situations where much less information is obtained: when the entries have a heavy-tailed distribution or when the variance profile has a specific structure. In this talk I discuss some recent discoveries in the latter regime. The topics include: a sharp description for the edge of a symmetric random matrix when its tail decays precisely like x^{-4} (the transition regime); a very weak condition for determining spectral outliers for finite rank perturbations of non-Hermitian random matrices with a banded variance profile; the smallest singular value for rectangular random matrix with entries in the domain of attraction of alpha-stable law; and on convergence to the circular law for ESDs of some nonhomogeneous matrices. The work employs recent concentration inequalities invented by Bandeira, Boedihardjo, van Handel and Brailovskaya. While satisfying results are obtained for some problems, a sharp understanding is still not obtained for other problems despite significant quantitative improvement.

• Feb 13
  Thursday, 3pm, 2-132

  Sasha Glazman

• Feb 17

  President's Day

• Feb 24

• Mar 3

• Mar 10

• Mar 17

• Mar 24

  Spring Break

• Mar 31

  Oren Yakir

• Apr 7

• Apr 14

• Apr 21

  Patriot's Day

• Apr 28

• May 5

• May 12