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Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting i...
In this talk, we mainly show some eigenvalue properties of second order Sturm-Liouville problems and third-order boundary value problems with both transmission conditions and eigenparameter-dependent ...
This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE RICCI FLOW     GEOMETRIC OPERATORS UNDER  FLOW       font style='font-size:12px;'> 2015/8/17
In this paper, we prove that the first eigenvalues of −∆ + cR (c ≥ 1 4 ) is nondecreasing under the Ricci flow. We also prove the monotonicity under the normalized Ricci &...
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear spe...
We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constrain...
Geometric Bounds for Eigenvalues of Markov Chains     Reversible markov chain  geometry       font style='font-size:12px;'> 2015/7/14
We develop bounds for the second largest eigenvalue and spectral gap of a reversible Markov chain. The bounds depend on geometric quantities such as the maximum degree, diameter and covering numbe...
On the Eigenvalues of Random Matrices     Random matrix  eigenvalue       font style='font-size:12px;'> 2015/7/14
On the Eigenvalues of Random Matrices.
This paper presents some new statistical tests and new conjectures regarding the correspondence between the eigenvalues of random unitary matrices and the zeros of Riemann’s zeta function. Global fe...
Linear Functionals of Eigenvalues of Random Matrices     Random  unitary matrix  the calculation function       font style='font-size:12px;'> 2015/7/14
.L.et 1% be a random r~x r~unitary matrix with distribution given by Haar measure on the unitary group. Using explicit monlerlt calculations, a general criterion is given for linear cornbinations of...
Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann's zeta function, a variety of physics...
Semi-linear equations and principal eigenvalues in unbounded domains.
Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemann...
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...

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