Universität zu Köln

Gallo, Gioele ORCID: 0000-0002-0818-9624 (2023). On some percolation problems in correlated systems. PhD thesis, Universität zu Köln.

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Abstract

In this thesis we explore the framework of the percolation theory and we analyse two models. We investigate the level set of the Gaussian free field on a supercritical Galton--Watson tree conditioned on non-extinction with random conductances, showing that the critical parameter h_* is deterministic and strictly positive, that the level set contains almost surely a transient component for some h>0 and it is stable under perturbation via small quenched noise. Then we study an infection model with recovery on fractal graphs as the Sierpinski gaskets and carpets and show the survival of the infection for small recovery parameter. To prove the result, we generalize the concept of Lsipschitz surface for the lattice to fractal graphs, and we show the existence and certain connectivity properties of what we call a Lipschitz Cutset.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Gallo, Gioele gioelegj@gmail.com https://orcid.org/0000-0002-0818-9624 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-717797
Date:	2023
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	Mathematics
Uncontrolled Keywords:	Keywords Language Percolation UNSPECIFIED Gaussian Field UNSPECIFIED Probability Theory UNSPECIFIED Gaussian free field UNSPECIFIED Fractal Graphs UNSPECIFIED Lipschitz Surface UNSPECIFIED Poisson random walks UNSPECIFIED
Date of oral exam:	24 October 2023
Referee:	Name Academic Title Drewitz, Alexander Prof. Dr. Moerters, Peter Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/71779