Random matrix theory over finite fields

By Jason E. Fulman. 2001

92 citations recorded by the source corpus.

The first part of this paper surveys generating functions methods in the study of random matrices over finite fields, explaining how they arose from theoretical need. Then we describe a probabilistic picture of conjugacy classes of the finite classical groups. Connections are made with symmetric function theory, Markov chains, Rogers-Ramanujan type identities, potential theory, and various measures on partitions.

Subfields: Geometry and Topology, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a5c05fa31881282ea67a7efd68d71d1aa557da21

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In Geometry and Topology

In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Integer sequences and matrices over finite fields (2006, methodology): “The generating function can be extracted from the proof of Theorem 1 in [6], which we present in section 2.”
Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements (2009, background): “There is a notion of cycle index for the orthogonal groups (see [ F1 ] or [F2] for background), and the cycle indices for the sum and dierence of the orthogonal groups factor.”
50 Years of Bailey’s Lemma (2009, background): “Indeed, after this paper was accepted for publication further advances in connection with the lemma were reported in [33, 34, 61].”
Combinatorial Stochastic Processes (2006, methodology): “BROWNIAN MOTION AND RELATED PROCESSES 5 • random partitions related to uniformly chosen invertible matrices over a finite field, as studied by Fulman [160]; • random maps, coalescing saddles, singularity analysis, and Airy phenomena, [81]; • random planar lattices and integrated superbrownian excurs”
Analytic Combinatorics (2009, background): “] The topic of random matrix theory over finite fields is blossomin g: see Fulman’s survey [272].”
Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture (2003, background): “A marvelous survey, making just these points and verifying them on nite groups of Lie type, is given in Fulman [ 43 ].”