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Permanental Point Processes on Real Tori

Jakob Hultgren (Institutionen för matematiska vetenskaper, matematik)
Göteborg : Chalmers University of Technology, 2016. - 78 s.
[Licentiatavhandling]

The main motivation for this thesis is to study real Monge-Ampère equations. These are fully nonlinear differential equations that arise in differential geometry. They lie at the heart of optimal transport and, as such, are related to probability theory, statistics, geometrical inequalities, fluid dynamics and diffusion equations. In this thesis we set up and study a thermodynamic formalism for a certain type of Monge-Ampère equations on real tori. We define a family of permanental point processes and show that their asymptotic behavior (when the number of particles tends infinity) is governed by Monge-Ampère equations.

Nyckelord: Point Processes, Monge-Ampère equations, Affine Manifolds



Denna post skapades 2016-05-18. Senast ändrad 2016-05-18.
CPL Pubid: 236658

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematisk analys
Geometri
Sannolikhetsteori och statistik

Chalmers infrastruktur

Examination

Datum: 2016-02-11
Tid: 13:15
Lokal: Room Euler, Mathematical Sciences, Chalmers Tvärgata 3, Chalmers
Opponent: Professor Mattias Jonsson, University of Michigan, US.