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Enumeration in Stochastic Processes ...

Jiang, Yuhan,

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Enumeration in Stochastic Processes and Polyhedral Geometry /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Enumeration in Stochastic Processes and Polyhedral Geometry // Yuhan Jiang.
Author:	Jiang, Yuhan,
Description:	1 electronic resource (106 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=32040331
ISBN:	9798280710900

Enumeration in Stochastic Processes and Polyhedral Geometry /
Jiang, Yuhan,

Enumeration in Stochastic Processes and Polyhedral Geometry /Yuhan Jiang. - 1 electronic resource (106 pages)

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

This dissertation explores the combinatorics of Markov chains and polyhedral geometry, with a focus on the asymmetric simple exclusion process (ASEP) and the Ehrhart theory of polytopes. The first part addresses the stationary distribution of stochastic models, including the open ASEP, the Arndt-Heinzel-Rittenberg (AHR) model and the doubly ASEP (DASEP). We give a two-layer simple random walk interpretation for the open ASEP model, a tableaux formula for the AHR model, and show that the DASEP exhibits homomesy phenomenon. The second part of the dissertation studies the Ehrhart theory of positroid polytopes and alcoved polytopes. We present combinatorial formulas for the h∗ -polynomials of positroid polytopes and alcoved polytopes. We also prove a connection between our shelling formula with decorated ordered set partitions.

English

ISBN: 9798280710900Subjects--Topical Terms:

515831
Mathematics.
Subjects--Index Terms:

Algebraic combinatorics

Enumeration in Stochastic Processes and Polyhedral Geometry /
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245 1 0 $a Enumeration in Stochastic Processes and Polyhedral Geometry / $c Yuhan Jiang.
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300 $a 1 electronic resource (106 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-12, Section: B.
500 $a Advisors: Williams, Lauren K. Committee members: Postnikov, Alexander; Defant, Colin; Harris, Joe.
502 $b Ph.D. $c Harvard University $d 2025.
520 $a This dissertation explores the combinatorics of Markov chains and polyhedral geometry, with a focus on the asymmetric simple exclusion process (ASEP) and the Ehrhart theory of polytopes. The first part addresses the stationary distribution of stochastic models, including the open ASEP, the Arndt-Heinzel-Rittenberg (AHR) model and the doubly ASEP (DASEP). We give a two-layer simple random walk interpretation for the open ASEP model, a tableaux formula for the AHR model, and show that the DASEP exhibits homomesy phenomenon. The second part of the dissertation studies the Ehrhart theory of positroid polytopes and alcoved polytopes. We present combinatorial formulas for the h∗ -polynomials of positroid polytopes and alcoved polytopes. We also prove a connection between our shelling formula with decorated ordered set partitions.
546 $a English
590 $a School code: 0084
650 4 $a Mathematics. $3 515831
650 4 $a Theoretical mathematics. $3 3173530
650 4 $a Statistics. $3 517247
650 4 $a Applied mathematics. $3 2122814
653 $a Algebraic combinatorics
653 $a Asymmetric simple exclusion process
653 $a Ehrhart theory
653 $a Markov chains
653 $a Polyhedral geometry
690 $a 0405
690 $a 0642
690 $a 0364
690 $a 0463
710 2 $a Harvard University. $b Mathematics. $e degree granting institution. $3 3765665
720 1 $a Williams, Lauren K. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-12B.
790 $a 0084
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=32040331