Related papers: The joint spectral radius is pointwise H\"older co…

Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…

We consider random $n\times n$ matrices $X$ with independent and centered entries and a general variance profile. We show that the spectral radius of $X$ converges with very high probability to the square root of the spectral radius of the…

Using a Tanaka representation of the local time for a class of superprocesses with dependent spatial motion, as well as sharp estimates from the theory of uniformly parabolic partial differential equations, the joint H\"older continuity in…

We use ergodic theory to prove a quantitative version of a theorem of M. A. Berger and Y. Wang, which relates the joint spectral radius of a set of matrices to the spectral radii of finite products of those matrices. The proof rests on a…

We obtain new partial results supporting the spectral set conjecture in dimension 1.

It is well known from the Perron-Frobenius theory that the spectral gap of a positive square matrix is positive. In this paper, we give a more quantitative characterization of the spectral gap. More specifically, using a complex extension…

We generalize the recent invariant polytope algorithm for computing the joint spectral radius and extend it to a wider class of matrix sets. This, in particular, makes the algorithm applicable to sets of matrices that have finitely many…

In various problems of control theory, non-autonomous and multivalued dynamical systems, wavelet theory and other fields of mathematics information about the rate of growth of matrix products with factors taken from some matrix set plays a…

The joint spectral radius of a pair of 2x2 real matrices $(A_0,A_1)\in M_2(\mathbb{R})^2$ is defined to be $r(A_0,A_1)= \limsup_{n\to\infty} \max \{\|A_{i_1}...A_{i_n}\|^{1/n}: i_j\in\{0,1\}\}$, the optimal growth rate of the norm of…

We consider a self-adjoint operator $T$ on a separable Hilbert space, with pure-point and simple spectrum with accumulations at finite points. Explicit conditions are stated on the eigenvalues of $T$ and on the bounded perturbation $V$…

Let ${\bf A} \in R^{n \times n}$ be a nonnegative irreducible square matrix and let $r({\bf A})$ be its spectral radius and Perron-Frobenius eigenvalue. Levinger asserted and several have proven that $r(t):=r((1{-}t) {\bf A} + t {\bf…

We prove that every locally pluripolar set on a compact complex manifold is pluripolar. This extends similar results in K\"ahler case.

This paper gives the pointwise H\"older (or multifractal) spectrum of continuous functions on the interval $[0,1]$ whose graph is the attractor of an iterated function system consisting of $r\geq 2$ affine maps on $\mathbb{R}^2$. These…

We consider the Quillen adjunction between fixed points and inflation in the context of equivariant module spectra over equivariant ring spectra, and give numerous examples including some based on geometric fixed points and some on the…

We introduce and study procedures and constructions in the theory of the joint spectral radius that are related to the spectral theory. In particular we devlop the theory of the scattered radical. Among applications we find some sufficient…

We prove three inequalities relating some invariants of sets of matrices, such as the joint spectral radius. One of the inequalities, in which proof we use geometric invariant theory, has the generalized spectral radius theorem of Berger…

Recently in hep-ph/0605035 and hep-ph/0608138, we have shown that primordial inflation can be embedded within the Minimal Supersymmetric Standard Model, while providing the right amplitude for the density perturbations and a tilted spectrum…

We study stability of spectral types for semi-infinite self-adjoint tridiagonal matrices under random decaying perturbations. We show that absolutely continuous spectrum associated with bounded eigenfunctions is stable under Hilbert-Schmidt…

Local oscillation of a function satisfying a H\"older condition is considered and it is proved that its growth is governed by a version of the Law of the Iterated Logarithm.

We prove that radial $SLE_\kappa$ and two-sided radial $SLE_\kappa$ are continuous at their terminal point.