5 papers
The Relative Variational Principle by Ledrappier and Walters: A survey
Anthony Quas
Ledrappier and Walters's article "A Relativised Variational Principle for Continuous Transformations", J. Lond. Math. Soc. (2) 16 (1977), no.3, 568-576) is a landmark in the develo…
Effective Gaps between singular values of non-stationary matrix products subject to non-degenerate noise
Sam Bednarski, Jonathan DeWitt, Anthony Quas
We study the singular values and Lyapunov exponents of non-stationary random matrix products subject to small, absolutely continuous, additive noise. Consider a fixed sequence of m…
Non-unique equilibrium measures and freezing phase transitions for matrix cocycles for negative
Reza Mohammadpour, Anthony Quas
We consider a one-step matrix cocycle generated by a pair of non-negative parabolic matrices and study the equilibrium measures for as runs over the real…
BCZ map is weakly mixing
Yitwah Cheung, Anthony Quas
The BCZ map was introduced in 2001 by Boca, Cobeli and Zaharescu as a tool to study the statistical properties of Farey sequences, whose relation to Riemann Hypothesis dates back t…
The Lightning Model
James Campbell, Alexandra Deane, Anthony Quas
We introduce a non-standard model for percolation on the integer lattice . Randomly assign to each vertex a potential, denoted , chosen indepe…