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Ergodic Problems in Random Environments: Polymers, Burgers Equation and Transport
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Ergodic Problems in Random Environments: Polymers, Burgers Equation and Transport. |
| 개인저자 | Li, Liying. |
| 단체저자명 | New York University. Mathematics. |
| 발행사항 | [S.l.]: New York University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 188 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-03B. Dissertation Abstract International |
| ISBN | 9781085670906 |
| 학위논문주기 | Thesis (Ph.D.)--New York University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-03, Section: B.
Advisor: Bakhtin, Yuri. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | We first study the asymptotic behavior of a time-discrete and space-continuous polymer model of a random walk in a random potential. We formulate the straightness estimate for the polymer measures and prove almost sure existence and uniqueness of polymer measures on one-sided infinite paths with given endpoint and slope, and interpretation of these infinite-volume Gibbs measures as thermodynamic limits. Moreover, we prove that marginals of polymer measures with the same slope and different endpoints are asymptotic to each other. Next we develop ergodic theory of the Burgers equation with positive viscosity and random kick forcing on the real line without any compactness assumptions. Namely, we prove a One Force -- One Solution principle, using the infinite-volume polymer measures to construct a family of stationary global solutions for this system, and proving that each of those solutions is a one-point pullback attractor on the initial conditions with the same spatial average. Using a straightness estimate uniform in temperature, we also prove that in the zero temperature limit, the infinite-volume polymer measures concentrate on the one-sided minimizers and that the associated global solutions of the viscous Burgers equation with random kick forcing converge to the global solutions of the inviscid equation.Finally, we present two examples of mixing stationary random smooth planar vector fields with bounded nonnegative components such that, with probability one, none of the associated integral curves possess an asymptotic direction. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
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