Zobrazeno 1 - 10
of 259
pro vyhledávání: '"TODD, MIKE"'
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of $\R^d$-valued observab
Externí odkaz:
http://arxiv.org/abs/2406.14807
Autor:
Todd, Mike, Zhao, Boyuan
We give a set of equivalent conditions for a potential on a Countable Markov Shift to have strong positive recurrence, which is also equivalent to having exponential decay of correlations. A key ingredient of our proofs is quantifying how the shift b
Externí odkaz:
http://arxiv.org/abs/2403.02092
Autor:
Holland, Mark, Todd, Mike
For a probability measure preserving dynamical system $(\mathcal{X},f,\mu)$, the Poincar\'e Recurrence Theorem asserts that $\mu$-almost every orbit is recurrent with respect to its initial condition. This motivates study of the statistics of the pro
Externí odkaz:
http://arxiv.org/abs/2401.13300
We present a general framework for weak convergence to decorated L\'evy processes in enriched spaces of c\`adl\`ag functions for vector-valued processes arising in deterministic systems. Applications include uniformly expanding maps and unbounded obs
Externí odkaz:
http://arxiv.org/abs/2310.00978
Autor:
Demers, Mark, Todd, Mike
We consider local escape rates and hitting time statistics for unimodal interval maps of Misiurewicz-Thurston type. We prove that for any point $z$ in the interval there is a local escape rate and hitting time statistics which is one of three types.
Externí odkaz:
http://arxiv.org/abs/2309.09624
For a class of potentials $\psi$ satisfying a condition depending on the roof function of a suspension (semi)flow, we show an EKP inequality, which can be interpreted as a H\"older continuity property in the weak${^*}$ norm of measures, with respect
Externí odkaz:
http://arxiv.org/abs/2308.14485
Autor:
Rousseau, Jerome, Todd, Mike
Given a dynamical system, we prove that the shortest distance between two $n$-orbits scales like $n$ to a power even when the system has slow mixing properties, thus building and improving on results of Barros, Liao and the first author. We also exte
Externí odkaz:
http://arxiv.org/abs/2209.06594
Autor:
Jurga, Natalia, Todd, Mike
Given a one-dimensional dynamical system we study its cover time, which quantifies the rate at which orbits become dense in the state space. Using transfer operator tools for dynamical systems with holes and inducing techniques, for a wide class of u
Externí odkaz:
http://arxiv.org/abs/2204.05008
We prove functional limit theorems for dynamical systems in the presence of clusters of large values which, when summed and suitably normalised, get collapsed in a jump of the limiting process observed at the same time point. To keep track of the clu
Externí odkaz:
http://arxiv.org/abs/2011.10153
Autor:
Iommi, Godofredo, Todd, Mike
Publikováno v:
Fundamenta Mathematicae 259, Vol.2 151--177 (2022)
Regularity properties of the pressure are related to phase transitions. In this article we study thermodynamic formalism for systems defined in non-compact phase spaces, our main focus being countable Markov shifts. We produce metric compactification
Externí odkaz:
http://arxiv.org/abs/2010.10250