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Based on this symmetric version, we give in section 3 a new criterion (Theorem 3.1) for the existence of a symmetric nonnegative matrix with prescribed spectrum, together with
It is common in applications to have a number of variables with a comparable order of magnitude with the number of observation samples; the analysis of the asymptotic
One approach is to investigate the absolute error in the self-normalized central limit theorem via Berry-Esseen bounds or Edgeworth expansions.. This has been done by many
We study lattice trees, lattice animals, and percolation on non-Euclidean lattices that correspond to regular tessellations of two- and three-dimensional hyperbolic space.. We
Then, we give sufficient conditions for a σ-finite measure to be invariant for this conditional process with any realization of the given Brownian motion.. In Section 4, we show
Section 3 gives estimates on the first and second moments of the killed branching random walk, while Section 4 contains the asymptotics on the tail distribution of the maximal
We consider the optimal mass transportation problem in R d with measurably parameterized marginals under conditions ensuring the existence of a unique optimal transport map.. We prove
Both algebras are presented by generators and relations, the first has a representation by q -difference operators on the space of symmetric Laurent polynomials in z and the second