Poisson-generic points | Vidéo | Carmin.tv

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Poisson-generic points

By Benjamin Weiss

Appears in collection : Jean-Morlet Chair 2020 - Conference: Diophantine Problems, Determinism and Randomness / Chaire Jean-Morlet 2020 - Conférence : Problèmes diophantiens, déterminisme et aléatoire

I will discuss a criterion for randomness of sequences of zeros and ones which is strictly stronger than normality, butholds for almost every sequence generated by i.i.d. random variables with distribution {1/2, 1/2}. Briefly put, the idea is count the number of times blocks of length n appear in the initial block of length $2^n$. I will also discuss an extension of this idea to toral automorphisms. (joint work with Yuval Peres)

Information about the video

Date of recording 25/11/2020
Date of publication 01/12/2020
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19690103
Cite this video Weiss, Benjamin (25/11/2020). Poisson-generic points. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19690103
URL https://dx.doi.org/10.24350/CIRM.V.19690103

Domain(s)

Bibliography

KAMAE, Teturo et XUE, Yu-Mei. An easy criterion for randomness. Sankhya A, 2015, vol. 77, no 1, p. 126-152. - https://doi.org/10.1007/s13171-014-0054-3
DE KONINCK, Jean-Marie, KÁTAI, Imre, et PHONG, Bui Minh. On strong normality. Uniform distribution theory, 2016, vol. 11, no 1, p. 59-78. - https://doi.org/10.1515/udt-2016-0005
HIRATA, Masaki. Poisson law for Axiom A diffeomorphisms. Ergodic Theory and Dynamical Systems, 1993, vol. 13, no 3, p. 533-556. - https://doi.org/10.1017/S0143385700007513

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