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Showing 1 to 2 of 2 for “"random polynomials"”.
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Random Sorting Networks, the Directed Landscape, and Random Polynomials
The first part of this thesis concerns random sorting networks. A sorting network is a shortest path from 12···n to n···21 in the Cayley graph of the symmetric group Sn generated by adjacent transpositions. We prove that in a uniform random n-element sorting network σn, all particle trajectories …
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The density of complex zeros of random sums
A random polynomial is a polynomial whose coefficients follow some probability distribution. The fundamental questions that need to be studied are the distribution and correlations between zeros, pairing between zeros and critical points, distribution values, and nodal surfaces. The computation of …