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High-Dimensional First Passage Perco...

The University of Chicago.

High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk./
作者:	Tang, Si.
面頁冊數:	1 online resource (81 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
標題:	Mathematics. -
電子資源:	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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035 $a AAI10615665
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100 1 $a Tang, Si. $3 1180880
245 1 0 $a High-Dimensional First Passage Percolation and Occupation Densities of Branching Random Walk.
264 0 $c 2017
300 $a 1 online resource (81 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: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Advisers: Steven P. Lalley; Antonio Auffinger.
502 $a Thesis (Ph.D.) $c The University of Chicago $d 2017.
504 $a Includes bibliographical references
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Statistics. $3 556824
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a The University of Chicago. $b Statistics. $3 1180881
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10615665 $z click for full text (PQDT)

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