getdoc7528. 135KB Jun 04 2011 12:04:31 AM
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For the case of 1 + 1 dimensions, the PT -symmetric Hamiltonian, although not Hermitian, has real eigenvalues for a range of values of the chemical potential µ , solving the
The study of the spectra of real symmetric (or Hermitian) matrices subordinated to a certain tree, and, in particular, of the number of distinct eigenvalues such acyclic matrices,
Further, we give some L¨ owner partial orders for compound matrices of Schur complements of positive semidefinite Hermitian matrices, and obtain some estimates for eigenvalues of
Key words: Bounded Lipschitz metric, large dimensional random matrix, eigenvalues, Wigner matrix, sample variance covariance matrix, Toeplitz matrix, Hankel matrix, cir- culant
In the paper [STW], it was shown that “a Brownian motion reflected on an independent time-reversed Brownian motion is again a Brownian motion” combining the fact that the
We first show that Brownian motions conditioned not to intersect have a good chance of being reasonably far apart, and conclude that the corresponding simple walks are also far
Keywords Brownian bridge, Brownian excursion, Brownian scaling, local time, Bessel process, zeros of Bessel functions, Riemann zeta function.. AMS subject classification 60J65,
coordinate systems this problem is reduced to the ǫ-covering time of the two-dimensional (flat) torus by a (standard) Brownian motion. In this paper we deal with manifolds of
