Special Colloquium

Speaker: Wai-Kit Lam (University of Minnesota)
Title: Random complex systems: examples and applications
Time: 2020-12-03 (Thu.)  09:00 - 10:00
Place: Auditorium, 6 Floor, Institute of Mathematics (NTU Campus)
Abstract: Random complex systems arise naturally in nature science, data science, etc. Although many of their formulations are seemingly simple, the underlying geometric and random structures turn out to be very profound and have been central topics in a number of interdisciplinary scientific areas. In this talk, I will discuss two fascinating examples. The first focuses on a percolation-type model from statistical physics defined on the integer lattice with nearest-neighbor edges equipped with nonnegative random edge weights. In this random environment, does there exist an infinite self-avoiding path such that it has finite total weight? We give an exact criterion in two dimensions for which such a path exists, and discuss some asymptotics related to this problem. The second part of the talk will address disorder universality in the so-called Approximate Message Passing (AMP) algorithm, popularly adapted in the study of statistical inference problems in recent years. I will discuss the performance of the AMP in the low-rank matrix recovery problem, and present results on universality of the convergence of a generalized algorithm regardless of the underlying random structures. Based on several joint works with W.-K. Chen, M. Damron, J. Hanson, D. Harper and X. Wang.
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