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On the Galois Group of generalized Laguerre polynomials
Newton polygon Galois group of big generalized laguerre polynomials
2014/12/25
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed α∈ℚ-ℤ <0 , Filaseta and Lam have shown that the nth deg...
Algebraic Properties of a Family of Generalized Laguerre Polynomials
Generalized laguerre polynomials algebraic properties negative integral value parameter
2014/12/24
We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers r,n≥0 , we conjecture that L(−1−n−r)n(x)=∑nj=0(nW...
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles
Random matrices Wishart ensemble Laguerre ensemble Jacobi ensemble Gram ensemble Hadamard ratio determinant invariance principle large deviations
2009/6/12
Asymptotic behavior of random determinants in the Laguerre, Gram and Jacobi ensembles.
Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes
Wishart and Laguerre ensembles and processes eigenvalues as diffusions non-colliding squared Bessel processes
2009/5/4
Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the La...
Hermite and Laguerre polynomials and matrix-valued stochastic
Hermite Laguerre polynomials matrix-valued stochastic processes
2009/3/19
We extend to matrix-valued stochastic processes, some well-known relations between real-valued diffusions and classical orthogonal polynomials, along with some recent results about Lévy processes and ...