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Shape fluctuations and random matrices. (English) Zbl 0969.15008
In a series of important problems in probability theory and combinatorics the variables of interest can be expressed in terms of Fredholm determinants. Asymptotic properties of the expressions of this type are deeply studied in the spectral theory of large random matrices. It is shown that certain characteristics of the random growth model asymptotically coincide with the distribution of the maximal eigenvalues of the ensemble of \(N\)-dimensional Hermitian matrices whose entries are jointly independent Gaussian random variables.

MSC:
15B52 Random matrices (algebraic aspects)
15A15 Determinants, permanents, traces, other special matrix functions
05E10 Combinatorial aspects of representation theory
15A18 Eigenvalues, singular values, and eigenvectors
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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