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This mostly expository note surveys and recovers a lower bound for the number of distinct eigenvalues of real symmetric matrices associated with a graph.. The relation is
For normal matrices in WPFn and those in WPFn for which the spectral radius is simple, we present approximating matrices that satisfy the strong P-F property and are polynomials
The main result of this paper is the following local limit theorem for the joint distribution of the vector ( |C1| ,. , |C k | ) in the Erd˝ os-Rényi random graph:.. Theorem 1.1
At the end of this note we show that (2) is not true in three dimensions, i.e., with probability one, the cut points of two independent three dimensional simple random walks
We present a short probabilistic proof of a weak convergence result for the number of cuts needed to isolate the root of a random recursive tree.. The proof is based on a
Key words: Large dimensional random matrix, eigenvalues, circulant matrix, symmetric circu- lant matrix, reverse circulant matrix, k circulant matrix, empirical spectral
With this choice of ζ, the genealogical tree is the CRT (see [1]), and the Brownian snake can be seen as an embedding of the CRT in R d. We can now give the definition of the ISE
In this paper, we consider Riemannian manifolds admitting a semi-symmetric non-metric connection such that U is a unit parallel vector field with respect to the Levi-Civita
