자료유형  

 학위논문

Control Number  

0016932541

International Standard Book Number  

9798379679088

Dewey Decimal Classification Number  

900

Main Entry-Personal Name  

Chio, Ivan.

Publication, Distribution, etc. (Imprint  

[S.l.] : Purdue University., 2020

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2020

Physical Description  

1 online resource(66 p.)

General Note  

Source: Dissertations Abstracts International, Volume: 84-12, Section: B.

General Note  

Advisor: Roeder, Roland K. W.

Dissertation Note  

Thesis (Ph.D.)--Purdue University, 2020.

Restrictions on Access Note  

This item must not be sold to any third party vendors.

Summary, Etc.  

요약Associated to any finite simple graph Γ is the chromatic polynomial PΓ(q) whose complex zeros are called the chromatic zeros of Γ. A hierarchical lattice is a sequence of finite simple graphs {Γn} ∞ n=0 built recursively using a substitution rule expressed in terms of a generating graph. For each n, let µn denote the probability measure that assigns a Dirac measure to each chromatic zero of Γn. Under a mild hypothesis on the generating graph, we prove that the sequence µn converges to some measure µ as n tends to infinity. We call µ the limiting measure of chromatic zeros associated to {Γn} ∞ n=0. In the case of the Diamond Hierarchical Lattice we prove that the support of µ has Hausdorff dimension two.The main techniques used come from holomorphic dynamics and more specifically the theories of activity/bifurcation currents and arithmetic dynamics. We prove a new equidistribution theorem that can be used to relate the chromatic zeros of a hierarchical lattice to the activity current of a particular marked point. We expect that this equidistribution theorem will have several other applications, and describe one such example in statistical mechanics about the Lee-Yang-Fisher zeros for the Cayley Tree.

Subject Added Entry-Topical Term  

Maps.

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Mapping.

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Phase transitions.

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Statistical physics.

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Diamonds.

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Statistical mechanics.

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Algebra.

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Polynomials.

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Theorems.

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Combinatorics.

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Mathematics.

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Physics.

Added Entry-Corporate Name  

Purdue University.

Host Item Entry  

Dissertations Abstracts International. 84-12B.

Host Item Entry  

Dissertation Abstract International

Electronic Location and Access  

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Control Number  

joongbu:643196