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SPLITTING FIELDS OF CHARACTERISTIC POLYNOMIALS OF RANDOM ELEMENTS IN ARITHMETIC GROUPS
SPLITTING FIELDS CHARACTERISTIC POLYNOMIALS RANDOM ELEMENTS ARITHMETIC GROUPS
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2015/8/26
We discuss rather systematically the principle, implicit in earlier works, that for a “random” element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the sp...
Average characteristic polynomials in the two-matrix model
Two-matrix model average characteristic polynomial
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2010/12/6
The two-matrix model is defined on pairs of Hermitian matrices (M1,M2) of size n × n by the probability measure 1 Zn exp (Tr(−V (M1) −W(M2) + M1M2)) dM1 dM2, where V and W are given poten...
Correlations of RMT Characteristic Polynomials and Integrability: Hermitean Matrices
non-Gaussian ensembles Hermitean random matrices tau-functions
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2010/4/6
Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation func...