Dynamical Systems and Analysis Seminar - Matthew Nicol
| Dates: | 8 June 2026 |
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| Times: | 14:00 - 14:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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Speaker: Matthew Nicol (University of Houston)
Title: Stable laws for slowly mixing dynamical systems
Abstract: Stable laws are a generalization of the central limit theorem. We investigate stable laws for observables f:X-->R on dynamical systems (T,X,m). They arise when a scaling of magnitude n^(1/alpha), alpha in (0,2), which is larger than sqrt(n) is necessary to give convergence of the scaled Birkhoff sums, n^(-1/alpha) sum_(j=0)^(n-1) f(T^j), to a non trivial distribution (a stable law). The usual sqrt(n) scaling of the central limit theorem corresponds to alpha = 2. Stable laws arise from two main mechanisms: the dynamical system is slowly mixing so that correlations are not summable; or the observable has infinite variance (heavy tails). We give results on the interplay of both mechanisms in a variety of slowly mixing intermittent type maps of the unit interval. In particular we consider heavy tailed observables of form f(x) = d(x,x_0)^(-1/alpha) for x_0 in 0,1 and investigate the stable law that results when x_0 != 0 or when x_0 = 0 (the fixed point). We also give some related results on stable laws for heavy tailed observables on polynomially mixing billiards.
Room: Frank Adams 1
Further information: https://personalpages.manchester.ac.uk/staff/yotam.smilansky/dynamics_analysis
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Frank Adams 1
Alan Turing Building
Manchester
