منابع مشابه
On Fredholm determinants in topology
For a finite simple graph G with adjacency matrix A, the Fredholm determinant ζ(G) = det(1 + A) is 1/ζG(−1) for the Bowen-Lanford zeta function ζG(z) = det(1 − zA)−1 of the graph. The connection graph G’ of G is a new graph which has as vertices the set V ′ of all complete subgraphs of G and where two such complete subgraphs are connected, if they have a non-empty intersection. More generally, ...
متن کاملOn the numerical evaluation of Fredholm determinants
Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in random matrix theory. Though their numerical values are of interest, there is no systematic numerical treatment of Fredholm determinants to be found in the literature. Instead, the few numerical evaluations th...
متن کاملIntermittency and Regularized Fredholm Determinants
We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator M has a decomposition sp(M) = σc ∪ σp where σc = [0, 1] is the continuous spectrum of M and σp is the pure point spectrum with no points of accumulation outside 0 and 1. W...
متن کاملNumerical Evaluation of Fredholm Determinants
Some significant quantities in mathematics and physics are most naturally expressed as the Fredholm determinant of an integral operator, most notably many of the distribution functions in random matrix theory. Though their numerical values are of interest, there is no systematic numerical treatment of Fredholm determinants to be found in the literature. Instead, the few numerical evaluations th...
متن کاملEvans function and Fredholm determinants
We explore the relationship between the Evans function, transmission coefficient and Fredholm determinant for systems of first-order linear differential operators on the real line. The applications we have in mind include linear stability problems associated with travelling wave solutions to nonlinear partial differential equations, for example reaction-diffusion or solitary wave equations. The...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1920
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1920-03328-8