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Multinomial Trees and Multinomial Pe...

Tienni, Michele,

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Multinomial Trees and Multinomial Percolation /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Multinomial Trees and Multinomial Percolation // Michele Tienni.
Author:	Tienni, Michele,
Description:	1 electronic resource (136 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
Contained By:	Dissertations Abstracts International86-12B.
Subject:	Mathematics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31845964
ISBN:	9798286442195

Multinomial Trees and Multinomial Percolation /
Tienni, Michele,

Multinomial Trees and Multinomial Percolation /Michele Tienni. - 1 electronic resource (136 pages)

Source: Dissertations Abstracts International, Volume: 86-12, Section: B.

We study multinomial percolation, which is bond percolation on a family of graphs ("blow-up graphs") defined in terms of a fixed graph G. We compute connection thresholds in terms of distances on G. Moreover, if the percolation probability is inversely proportional to the blow-up multiplicity, there is a phase transition above which a giant component emerges. We show that many properties of the giant component can be computed using an analytic function with variables indexed by the vertices of G. Moreover, we find that the giant component gives rise to a natural field on G. As the blow-up multiplicity grows, we show that this field converges to a Gaussian field, and its covariance is given by the square of a massive Green's function on G.The main tool to prove the results above is the combinatorics of trees on blowup graphs ("multinomial trees"). To this end, the first half of this thesis is dedicated to the theory of multinomial trees. This includes two parts. Enumeration results show that the asymptotic growth of such trees are given by relative entropies of certain distributions on G. Analytic results show that the multivariate exponential generating function for rooted multinomial trees has analytic properties that can be formulated in terms of a massive Laplacian operator on G.

English

ISBN: 9798286442195Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Generating function

Multinomial Trees and Multinomial Percolation /
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100 1 $a Tienni, Michele, $e author. $3 3822991
245 1 0 $a Multinomial Trees and Multinomial Percolation / $c Michele Tienni.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2025
300 $a 1 electronic resource (136 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Kenyon, Richard Committee members: Smart, Charles; Neitzke, Andrew.
502 $b Ph.D. $c Yale University $d 2025.
520 $a We study multinomial percolation, which is bond percolation on a family of graphs ("blow-up graphs") defined in terms of a fixed graph G. We compute connection thresholds in terms of distances on G. Moreover, if the percolation probability is inversely proportional to the blow-up multiplicity, there is a phase transition above which a giant component emerges. We show that many properties of the giant component can be computed using an analytic function with variables indexed by the vertices of G. Moreover, we find that the giant component gives rise to a natural field on G. As the blow-up multiplicity grows, we show that this field converges to a Gaussian field, and its covariance is given by the square of a massive Green's function on G.The main tool to prove the results above is the combinatorics of trees on blowup graphs ("multinomial trees"). To this end, the first half of this thesis is dedicated to the theory of multinomial trees. This includes two parts. Enumeration results show that the asymptotic growth of such trees are given by relative entropies of certain distributions on G. Analytic results show that the multivariate exponential generating function for rooted multinomial trees has analytic properties that can be formulated in terms of a massive Laplacian operator on G.
546 $a English
590 $a School code: 0265
650 4 $a Mathematics. $3 515831
650 4 $a Statistical physics. $3 536281
650 4 $a Applied mathematics. $3 2122814
653 $a Generating function
653 $a Laplacian operator
653 $a Percolation
653 $a Random graph
653 $a Random walk
653 $a Spanning tree
690 $a 0405
690 $a 0217
690 $a 0364
710 2 $a Yale University. $b Mathematics. $e degree granting institution. $3 3822989
720 1 $a Kenyon, Richard $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0265
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31845964