We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable nondegenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theo...

We compare computational cost and accuracy between two different approaches of dispersion analysis. One is the conventional Monte Carlo method and the other being the Perron-Frobenius operator approach, that directly propagates the joint probability density function using Liouville equation. It is shown that with same computational budget, Perron-Frobenius operator approach rewards better accur...

We prove that the Frobenius–Perron operator of the cusp map F : [−1, 1] → [−1, 1], F (x) = 1 − 2 √ |x| (which is an approximation of the Poincaré section of the Lorenz attractor) has no analytic eigenfunctions corresponding to eigenvalues different from 0 and 1. We also prove that the spectrum of the Frobenius–Perron operator in the space of real-analytic functions on [0, 1] as well as in the s...

Markov chain Monte Carlo, or MCMC, is a way to sample probability distributions that cannot be sampled practically using direct samplers. Most complex probability distributions in more than a few variables are are sampled in this way. For us, a stationary Markov chain is a random sequence X1, X2, . . ., where Xk+1 = M(Xk, ξk), where M(x, ξ) is a fixed function and the inputs ξ are i.i.d. random...

A cycle expansion technique for discrete sums of several PF operators, similar to the one used in the standard classical dynamical zeta-function formalism is constructed. It is shown that the corresponding expansion coefficients show an interesting universal behavior, which illustrates the details of the interference between the particular mappings entering the sum.

In recent years there has been interest in a theorem on positive definite matrices known as Lyapunov's theorem. Several authors have proved generalizations of this theorem, (WIELANDT [29J, TAUSSKY [24J, [25J, [26J , OSTROWSKISCHNEIDER [20J, GIVENS [10J, CARLSON-SCHNEIDER [3J, CARLSON [4J) . Lyapunov's theorem and its generalizations have become known as inertia theorems. In this note we shall u...

A matrix A can be tested to determine whether it is eventually positive by ex1 amination of its Perron-Frobenius structure, i.e., by computing its eigenvalues and left and right 2 eigenvectors for the spectral radius ρ(A). No such “if and only if” test using Perron-Frobenius prop3 erties exists for eventually nonnegative matrices. The concept of a strongly eventually nonnegative 4 matrix was wa...

We consider subshifts of nite type on the symbol space generated by incidence matrices over a countably innnite alphabet. We extend the deenition of topological pressure to this context and, as our main result, we construct a new class of Gibbs states of HH older continuous potentials on these symbol spaces. We establish some basic stochastic properties of these Gibbs states: exponential decay ...