Abstract We expand upon work from many hands on the decomposition of nuclear maps. Such maps can be characterised by their ability to approximately written as composition and matrices. Under certain conditions (such quasidiagonality), we find a whose behave nicely, preserving multiplication up an arbitrary degree accuracy being constructed order-zero (as in definition dimension). investigate th...

Abstract We prove that if $f(n)$ is a Steinhaus or Rademacher random multiplicative function, there almost surely exist arbitrarily large values of $x$ for which $|\sum _{n \leq x} f(n)| \geq \sqrt{x} (\log \log x)^{1/4+o(1)}$. This the first such bound grows faster than $\sqrt{x}$, answering question Halász and proving conjecture Erd?s. It plausible exponent $1/4$ sharp in this problem. The pr...

This paper is concerned with uniform convergence in the multiplicative ergodic theorem on aperiodic subshifts. If such a subshift satisfies a certain condition, originally introduced by Boshernitzan, every locally constant SL(2,R)-valued cocycle is uniform. As a consequence, the corresponding Schrödinger operators exhibit Cantor spectrum of Lebesgue measure zero. An investigation of Boshernitza...