Matija Vidmar: Noise Boolean algebras: classicality, blackness and spectral independence

Date of publication: 3. 5. 2022
Seminar for probability, statistics, and financial mathematics
Predavalnica 3.06 na FMF, Jadranska 21, Ljubljana.

V četrtek, 5. 5. 2022 ob14:15, bo v predavalnici 3.06 na FMF, Jadranska 21, potekalo predavanje Matije Vidmarja z naslovom Noise Boolean algebras: classicality, blackness and spectral independence.

Povzetek: Informally speaking, a noise Boolean algebra is an aggregate of information complexes, subject to independence properties relative to an underlying notion of chance. More formally, it is a distributive sublattice of the lattice of all sub-sigma-fields of a given probability measure, each element of which admits an independent complement.

A noise Boolean algebra is classical (resp. black) when all its random variables are stable (resp. sensitive) under infinitesimal perturbations of its basic ingredients. For instance, the Wiener and Poisson noises are classical, but certain noises of percolation and coalescence are black. We shall see that classicality and blackness are respectively characterized by existence and non-existence of certain so-called spectral independence probabilities, which we shall introduce. Based on:

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