Random matrix theory over finite fields

DOI10.1090/S0273-0979-01-00920-XzbMath0984.60017arXivmath/0003195OpenAlexW2072374043MaRDI QIDQ2761195

Jason Fulman

Publication date: 17 December 2001

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0003195

zbMATH Keywords

conjugacy classesMarkov chainspotential theoryRogers-Ramanujan type identitiessymmetric function theorygenerating functions methods

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15)

Related Items (40)

Bounds on the number and sizes of conjugacy classes in finite Chevalley groups with applications to derangements ⋮ Infinite 𝑝-adic random matrices and ergodic decomposition of 𝑝-adic Hua measures ⋮ Conjugacy class properties of the extension of \(\text{GL}(n,q)\) generated by the inverse transpose involution. ⋮ A super-class walk on upper-triangular matrices ⋮ Closed expressions for averages of set partition statistics ⋮ Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture ⋮ Solving p-adic polynomial systems via iterative eigenvector algorithms ⋮ Statistical enumeration of groups by double cosets ⋮ Binomial transforms and integer partitions into parts of \(k\) different magnitudes ⋮ Polynomial matrices, splitting subspaces and Krylov subspaces over finite fields ⋮ Super-linear convergence in the p -adic QR-algorithm ⋮ On the distribution of equivalence classes of random symmetric p‐adic matrices ⋮ A family of measures on symmetric groups and the field with one element ⋮ HALF-SPACE MACDONALD PROCESSES ⋮ Nearly self-conjugate integer partitions ⋮ The Smith Normal Form Distribution of A Random Integer Matrix ⋮ The perfect order subset conjecture for simple groups. ⋮ On the distribution of eigenspaces in classical groups over finite rings. ⋮ Unnamed Item ⋮ Finite traces and representations of the group of infinite matrices over a finite field ⋮ Cycle indices for finite orthogonal groups of even characteristic ⋮ ON THE DISTRIBUTION OF ORDERS OF FROBENIUS ACTION ON ^-TORSION OF ABELIAN SURFACES ⋮ Distribution of matrices with restricted entries over finite fields ⋮ Splitting fields for characteristic polynomials of matrices with entries in a finite field ⋮ Limits and fluctuations of \(p\)-adic random matrix products ⋮ Splitting behavior of \(S_n\)-polynomials ⋮ A probabilistic interpretation of the Macdonald polynomials ⋮ The Eulerian generating function of \(q\)-derangements ⋮ Observables of Macdonald processes ⋮ Cohen-Lenstra distributions via random matrices over complete discrete valuation rings with finite residue fields ⋮ Unnamed Item ⋮ Dimension-independent statistics of 𝐺𝑙_{𝑛}(𝔽_{𝕢}) via character polynomials ⋮ Law of large numbers for infinite random matrices over a finite field ⋮ Infinite-dimensional groups over finite fields and Hall-Littlewood symmetric functions ⋮ Birational permutations ⋮ A probabilistic approach to conjugacy classes in the finite symplectic and orthogonal groups ⋮ Some new results in random matrices over finite fields ⋮ Elementary divisors and determinants of random matrices over a local field. ⋮ Finite affine groups: cycle indices, Hall-Littlewood polynomials, and probabilistic algorithms ⋮ Stein's method and the rank distribution of random matrices over finite fields

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