The CUNY Probability Seminar is typically held on Tuesdays from 4:15 to 5:15 pm at the CUNY Graduate Center Math Department in room 5417. The exact dates, times and locations are mentioned below. If you want to talk at the seminar, or want to be added to/removed from the seminar mailing list, then please contact the Seminar Coordinator.
Toby Johnson (https://www.math.csi.cuny.edu/~tobiasljohnson/)
Tuesday, September 25, 2018, 4:30-5:30 (please note that this talk starts at 4:30, not 4:15!)
Speaker: Qiang Zeng, Queens College
Title: Replica Symmetry Breaking for mean field spin glass models
Abstract: Mean field spin glass models were introduced as an approximation of the physical short range models in the 1970s. The typical mean field models include the Sherrington-Kirkpatrick (SK) model, the (Ising) mix p-spin model and the spherical mixed p-spin model. Starting in 1979, the physicist Giorgio Parisi wrote a series of groundbreaking papers introducing the idea of replica symmetry breaking (RSB), which allowed him to predict a solution for the SK model by breaking the symmetry of replicas infinitely many times at low temperature. In this talk, we will show that Parisi’s prediction holds at zero temperature for the more general mixed p-spin model. On the other hand, we will show that there exist two-step RSB spherical mixed p-spin glass models at zero temperature, which are the first natural examples beyond the replica symmetric, one-step RSB and Full-step RSB phases.
This talk is based on joint works with Antonio Auffinger (Northwestern University) and Wei-Kuo Chen (University of Minnesota).
Tuesday, October 2, 2018, 4:15-5:15
Speaker: Erik Slivken, University of Paris VII
Tuesday, October 9, 2018, 4:15-5:15
Speaker: Matthew Junge, Duke University
Title: Diffusion-Limited Annihilating Systems
Abstract: We study a two-type annihilating system in which particles are placed with equal density on the integer lattice. Particles perform simple random walk and annihilate when they contact a particle of different type. The occupation probability of the origin was known to exhibit anomalous behavior in low-dimension when particles have equal speeds. Describing the setting with asymmetric speeds has been open for over 20 years. We prove a lower bound that matches physicists’ conjectures and discuss partial progress towards an upper bound. Joint with Michael Damron, Hanbaek Lyu, Tobias Johnson, and David Sivakoff.
Tuesday, October 16, 2018, 4:15-5:15
Speaker: Xin Sun, Columbia University
Tuesday, October 23, 2018, 4:15-5:15
Speaker: Ofer Zeitouni, Weizmann Institute/NYU
Tuesday, October 30, 2018, 4:15-5:15
Speaker: Ruojun Huang, NYU
Tuesday, September 4, 2018, 4:15-5:15
Speaker: Philip Matchett Wood, U. Wisconsin
Title: Limiting eigenvalue distribution for the non-backtracking matrix of an Erdős-Rényi random graph
Abstract: A non-backtracking random walk on a graph is a directed walk with the constraint that the last edge crossed may not be immediately crossed again in the opposite direction. This talk will give a precise description of the eigenvalues of the adjacency matrix for the non-backtracking walk when the underlying graph is an Erdős-Rényi random graph on n vertices, where edges present independently with probability p. We allow p to be constant or decreasing with n, so long as tends to infinity. The key ideas in the proof are partial derandomization, applying the Tao-Vu Replacement Principle in a novel context, and showing that partial derandomization may be interpreted as a perturbation, allowing one to apply the Bauer-Fike Theorem. Joint work with Ke Wang at HKUST (Hong Kong University of Science and Technology).