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Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices
Fluctuations of the extreme eigenvalues finite rank deformations of random matrices
2010/11/26
Consider a deterministic self-adjoint matrix Xn with spectral measure converging to a compactly supported probability measure, the largest and smallest eigenvalues converging to the edges of the limit...
Free probability, Planar algebras, Subfactors and Random Matrices
Free probability von Neumann algebra random matrix subfactor planar algebra
2010/11/30
To a planar algebra P in the sense of Jones we associate a natural non-commutative ring, which can be viewed as the ring of non-commutative polynomials in several indeterminates, invariant under a sym...
Large deviations of the maximal eigenvalue of random matrices
Large deviations maximal eigenvalue random matrices
2010/12/3
We present detailed computations of the ’at least finite’ terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in β-ensembles,with any polynomial potential. β...
Dichotomy theorems for random matrices and closed ideals of operators on $\big(\bigoplus_{n=1}^\infty\ell_1^n \big)_{\mathrm{c}_0}$
Dichotomy random matrices closed ideals of operators
2010/12/7
We prove two dichotomy theorems about sequences of operators into L1 given by random matrices. In the second theorem we assume that the entries of each random ma-trix form a sequence of independent, s...
Toy Model for Large Non-Symmetric Random Matrices
Singular Values Rectangular Random Matrices Free Random Matrix Theory Vector Models
2010/4/28
Non-symmetric rectangular correlation matrices occur in many problems in economics. We test the method of extracting statistically meaningful correlations between input and output variables of large d...
Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case
Double scaling limits minimal (2m,1) models random matrices
2010/4/2
In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the int...
Estimating generalised Lyapunov exponents for products of random matrices
random matrices large-deviation regime fluid flows
2010/4/7
We discuss several techniques for the evaluation of the generalised Lyapunov exponents which characterise the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorit...
Lock step walker model is a one-dimensional integer lattice walker model in discrete time. Suppose that initially there are infinitely many walkers on the non-negative even integer sites. At each tic...