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Freezing and decorated Poisson point processes

By Ofer Zeitouni

Appears in collection : Recent models in random media / Modèles récents en milieu aléatoire

The freezing in the title refers to a property of point processes: let $\left ( X_i \right )_{i\geq 1}$ denote a point process which is locally finite and has finite maximum. For a function f continuous of compact support, define $Z_f=f\left ( X_1 \right )+f\left ( X_2 \right )+....$ We say that freezing occurs if the Laplace transform of $Z_f$ depends on f only through a shift. I will discuss this notion and its equivalence with other properties of the point process. In particular, such freezing occurs for the extremal process in branching random walks and in certain versions of the (discrete) two dimensional GFF. Joint work with Eliran Subag

Information about the video

Date of recording 02/06/2014
Date of publication 16/06/2014
Institution CIRM
Licence CC BY NC ND
Language English
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18503803
Cite this video Zeitouni, Ofer (02/06/2014). Freezing and decorated Poisson point processes. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18503803
URL https://dx.doi.org/10.24350/CIRM.V.18503803

Domain(s)

Probability

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