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The extreme ranks, i.e., the maximal and minimal ranks, are established for the general Hermitian solution as well as the general skew-Hermitian solution to the classical
A key tool to obtain these bounds is using some Hermitian matrices which are, in the sense of Loewner matrix ordering, below the Hermitian part of A or, more generally, below
The converse is also studied: given an SDD matrix C with the structure of a k -subdirect sum and positive diagonal entries, it is shown that there are two SDD matrices whose
In the case of a partial TP matrix, the graph of whose specified entries is a sym- metrically placed cycle, as given in (1.1), the necessary conditions for a TP completion are the
We verify in some cases convergence of scaling limits of these models to a pair of super-Brownian motions interacting through their collision local times, constructed by Evans
In this paper we will study the spectral properties of Wigner real symmetric and Hermitian random matrices in the case when the matrix entries have heavy tails of distribution..
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to
Key words: Interacting Brownian motions, Brownian intersection local times, large deviations, occupation measure, Gross-Pitaevskii formula.. AMS 2000 Subject Classification:
