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High-Dimensional First Passage Perco...
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The University of Chicago.
High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
Record Type:
Language materials, manuscript : Monograph/item
Title/Author:
High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk./
Author:
Tang, Si.
Description:
1 online resource (81 pages)
Notes:
Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:
Dissertation Abstracts International79-02B(E).
Subject:
Mathematics. -
Online resource:
click for full text (PQDT)
ISBN:
9780355234916
High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
Tang, Si.
High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
- 1 online resource (81 pages)
Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Thesis (Ph.D.)
Includes bibliographical references
We prove limiting theorems for two particles systems, first passage percolation (FPP) and branching random walk (BRW). For the FPP model on $\mathbb Z.
Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018
Mode of access: World Wide Web
ISBN: 9780355234916Subjects--Topical Terms:
527692
Mathematics.
Index Terms--Genre/Form:
554714
Electronic books.
High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
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High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
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1 online resource (81 pages)
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online resource
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Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
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Advisers: Steven P. Lalley; Antonio Auffinger.
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Thesis (Ph.D.)
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The University of Chicago
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2017.
504
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Includes bibliographical references
520
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We prove limiting theorems for two particles systems, first passage percolation (FPP) and branching random walk (BRW). For the FPP model on $\mathbb Z.
520
$a
{d}$,we show that if the passage times have finite mean, then $\displaystyle \lim_{d \to \infty} \frac{\mu(\mathbf e_{1}) d}{\log d} = \frac{1}{2a}$, where $\mu(\mathbf e_{1})$ is the time constant in the $\mathbf e_{1}$ direction and $a \in [0,\infty]$ is a constant that depends only on the distribution of the passage times at $0$. For the same class of distributions, we also prove that the limit shape is not an Euclidean ball, nor a $d$-dimensional cube or diamond, when $d$ is large enough.
520
$a
For the BRW model, we prove that the rescaled occupation densities of a one-dimensional critical BRW converge to the occupation densities of a super-Brownian motion. We further show that the limiting occupation density process is a pure-jump subordinator in $\mathcal C_{0}(\mathbb R)$, whose jumps are rescaled versions of i.i.d. copies of an Integrated super-Brownian Excursion (ISE) density, weighted by the jump sizes of a real-valued stable-$\frac{1}{2}$ subordinator.
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Ann Arbor, Mich. :
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ProQuest,
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2018
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Mode of access: World Wide Web
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Mathematics.
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527692
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556824
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Electronic books.
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ProQuest Information and Learning Co.
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The University of Chicago.
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http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10615665
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click for full text (PQDT)
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