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Asymptotic spectral distributions of distance-k graphs of Cartesian product graphs

Yuji Hibino, Hun Hee Lee, Nobuaki Obata (2013)

Colloquium Mathematicae

Let G be a finite connected graph on two or more vertices, and G [ N , k ] the distance-k graph of the N-fold Cartesian power of G. For a fixed k ≥ 1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of G [ N , k ] . The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.

Asymptotic stability condition for stochastic Markovian systems of differential equations

Efraim Shmerling (2010)

Mathematica Bohemica

Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by d X ( t ) = A ( ξ ( t ) ) X ( t ) d t + H ( ξ ( t ) ) X ( t ) d w ( t ) , where ξ ( t ) is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.

Asymptotic stability in L¹ of a transport equation

M. Ślęczka (2004)

Annales Polonici Mathematici

We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.

Asymptotic stability in the Schauder fixed point theorem

Mau-Hsiang Shih, Jinn-Wen Wu (1998)

Studia Mathematica

This note presents a theorem which gives an answer to a conjecture which appears in the book Matrix Norms and Their Applications by Belitskiĭ and Lyubich and concerns the global asymptotic stability in the Schauder fixed point theorem. This is followed by a theorem which states a necessary and sufficient condition for the iterates of a holomorphic function with a fixed point to converge pointwise to this point.

Asymptotic stability of a linear Boltzmann-type equation

Roksana Brodnicka, Henryk Gacki (2014)

Applicationes Mathematicae

We present a new necessary and sufficient condition for the asymptotic stability of Markov operators acting on the space of signed measures. The proof is based on some special properties of the total variation norm. Our method allows us to consider the Tjon-Wu equation in a linear form. More precisely a new proof of the asymptotic stability of a stationary solution of the Tjon-Wu equation is given.

Asymptotic study of canonical correlation analysis: from matrix and analytic approach to operator and tensor approach.

Jeanne Fine (2003)

SORT

Asymptotic study of canonical correlation analysis gives the opportunity to present the different steps of an asymptotic study and to show the interest of an operator and tensor approach of multidimensional asymptotic statistics rather than the classical, matrix and analytic approach. Using the last approach, Anderson (1999) assumes the random vectors to have a normal distribution and the non zero canonical correlation coefficients to be distinct. The new approach we use, Fine (2000), is coordinate-free,...

Asymptotically cyclic quasianalytic contractions

László Kérchy, Attila Szalai (2014)

Studia Mathematica

The study of quasianalytic contractions, motivated by the hyperinvariant subspace problem, is continued. Special emphasis is put on the case when the contraction is asymptotically cyclic. New properties of the functional commutant are explored. Analytic contractions and bilateral weighted shifts are discussed as illuminating examples.

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