Séminaire Datashape
On zeta functions and their application to the study of the topology of superlevel sets of stochastic processes
23
Sep. 2021
 Intervenant : Daniel Perez Institution : LMO Heure : 11h00 - 12h00 Lieu : 2L8

We introduce the notion of stochastic zeta function, which for some classes of processes share many properties with their counterparts in analytic number theory. These zeta functions, defined in terms of the barcode, are related to a dual variable counting the number of bars in the bars in the barcode of length $\geq \varepsilon$. A "prime number theorem" can then be proved for this dual variable in terms of the zeta function of the considered process.