We consider the class of quantum spin chains with arbitrary Uq(sl2)-invariant nearest neighbor interactions, sometimes called SUq(2) for the quantum deformation of SU(2), for q > 0. We derive sufficient conditions for the Hamiltonian to satisfy the property we call Ferromagnetic Ordering of Energy Levels. This is the property that the ground state energy restricted to a fixed total spin subspac...

When the initial and transition probabilities of a finite Markov chain in discrete time are not well known, we should perform a sensitivity analysis. This is done by considering as basic uncertainty models the so-called credal sets that these probabilities are known or believed to belong to, and by allowing the probabilities to vary over such sets. This leads to the definition of an imprecise M...

We study ergodicity of bounded, sub-additive and non-negatively homogeneous maps on finite dimensional spaces which we call upper transition operators. We show that ergodicity coincides with the necessary and sufficient condition for a generalised Perron-Frobenius theorem for upper transition operators. We show that ergodicity is equivalent with regular absorningness of the upper transition ope...

0. Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Part I. Renewal theorems in symbolic dynamics . . . . . . . . . . . . 1. Background: Shifts, suspension flows, thermodynamic formalism . 2. 3. 4. 5. 6. 7. 1 5 5 Renewal measures and renewal theorems . . . . . . . . . . . . . . 7 A modification for finite sequences . . . . . . . . . . . . . . . . . 10 Equidistribution theo...

We consider multitype branching processes arising in the study of random laminations of the disk. We classify these processes according to their subcritical or supercritical behavior and provide Kolmogorov-type estimates in the critical case corresponding to the random recursive lamination process of [1]. The proofs use the infinite dimensional Perron-Frobenius theory and quasistationary distri...

We prove theorems of Perron–Frobenius type for positive elements in partially ordered topological algebras satisfying certain hypotheses. We show how some of our results relate to known results on Banach algebras. We give examples and state some open questions. © 2005 Elsevier Inc. All rights reserved. AMS classification: 47A10; 46H35; 47B65; 15A48

We study a family of chaotic maps with limit cases the tent map and the cusp map (the cusp family). We discuss the spectral properties of the corresponding Frobenius–Perron operator in different function spaces including spaces of analytic functions. A numerical study of the eigenvalues and eigenfunctions is performed.

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching aroun...