Permanental Point Processes on Real Tori

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

NATURVETENSKAP  -- Matematik -- Geometri (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Geometry (hsv//eng)

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Nyckelord

Point Processes

Monge-Ampère equations

Affine Manifolds

Point Processes

Publikations- och innehållstyp

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