Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science

2016-08-29

2016

Μπάζμπας Μιχαήλ

Δημήτρης Χελιώτης Αναπλ. Καθηγητής

Θεωρία διήθησης

Greek

Percolation theory

In this particular thesis we will present the percolation model on lattices. We
will define the model, our main objects of study and we will prove certain
properties as well as some technical tools. After that we will divide our model
in three phases (subcritical , critical, supercritical).The critical
probability will help us characterize every phase. Next we will study the three
phases and we will provide the most essential theorems of every one of them,
furthermore we will see how some of our main objects of study, e.x. the
percolation probability and the mean size of an open cluster, alternate through
every phase. Finally we will prove some exact results of bond percolation on
the square lattice and we will present the RSW theorem. In the end we will see
how percolation is correlated with small world graphs in order to model and
solve epidemic problems

Percolation theory, Statistical mechanics, Probability on lattices, Percolation probability, RSW theorem

No

0

No

7

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File access is restricted.

https://pergamos.lib.uoa.gr/uoa/dl/object/1317977