# Tropical Probability Theory

**Lecturer:**Rostislav Matveev**Date:**Wednesday, 11.00-12.30**Room:**MPI MiS A3 02

## Abstract

There are several lines of research studying entropy-like quantities for a collection of random variables. Many constructions of such quantities are proposed, that satisfy certain conditions or have desired properties. Tropical probability proposes to study entropy-like quantities in bulk. The closest analogy will be the relation between calculus and functional analysis. Very roughly, entropy-like quantity associates a value to the collection of random variables. This association is required to be non-negative, additive (with respect to taking iid copies) and continuous with respect to some natural topology. The word "tropical" refers to the certain "tropicalization" procedure, in spirit very similar to the "tropicalization" as used in algebraic geometry. Tropicalization is used for the construction of the "tropical cone" of diagrams of probability spaces -- a subcone in a certain Banach space and topology thereupon. The dual of the tropical cone is the cone of entropy-like quantities. The ultimate goal would be to understand the space of all entropy-like quantities, from which one could then pick those needed for particular applications, such as causal inference, info decomposition, etc. This area of research is little understood, open questions are behind every corner, and conjectures are abundant.To keep informed about changes to this lecture subscribe to lecture mailinglist

## Regular lectures: Summer semester 2022

**Representation theory of finite groups**- Arthur Bik
- Thursdays 7:30-9:00 and Fridays 9:15-10:45, SG 3-10
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**Bielefeld-Leipzig online seminar: Mathematics of Machine Learning**- Benjamin Gess
- Wednesdays 16:15-17:45, Videobroadcast

**Mathematical methods in biology and neurobiology**- Jürgen Jost
- Friday, 14.00, MPI MiS E1 05 (Leibniz)
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**Tropical Probability Theory**- Rostislav Matveev
- Wednesday, 11.00-12.30, MPI MiS A3 02
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**Non-backtracking operators of graphs**- Raffaella Mulas, Leo Torres
- Mondays at 3pm, starting May 2, MPI MiS A3 01
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**Recent developments in discrete Ricci curvature**- Florentin Münch
- Wednesday, 15.00, MPI MiS A3 01
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**First-order and online optimization methods**- Katerina Papagiannouli, André Uschmajew
- Lectures: Tuesdays 11:00-12:30, Exercises (biweekly): Tuesdays 14:00-15:00, MPI MiS G3 10
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**Spin Glasses**- Tobias Ried
- tba, Videobroadcast
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**IMPRS Ringvorlesung****Lecturers:**Bernd Rosenow, Felix Otto, Sayan Mukherjee**Date**: usually Thursdays, 9.15 - 10.45, see schedule for**divergent dates and times**and more info**Room:**MPI MiS, Leibniz-Hörsaal, also hybrid- To keep informed about changes to this lecture subscribe to lecture mailinglist