University of Birmingham > Talks@bham > Combinatorics and Probability Seminar > Roots of random polynomials near the unit circle

Roots of random polynomials near the unit circle

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It is a well-known (but perhaps surprising) fact that a polynomial with independent random coefficients has most of its roots very close to the unit circle. Using a probabilistic and combinatorial perspective, we understand the behavior of roots of random polynomials exceptionally close to the unit circle and prove several limit theorems; these results resolve several conjectures of Shepp and Vanderbei. We will also discuss how our techniques provide a heuristic, combinatorial explanation for why random polynomials tend to have most roots near the unit circle. Based on joint work with Julian Sahasrabudhe.

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https://bham-ac-uk.zoom.us/j/83022685017?pwd=L1RQclI2dmIvL2RXeUNCblpuanlBUT09

Meeting ID: 830 2268 5017 Passcode: 101833

This talk is part of the Combinatorics and Probability Seminar series.

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