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Time Evolution of the Kardar-Parisi-...

Ghosal, Promit.

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Time Evolution of the Kardar-Parisi-Zhang Equation.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Time Evolution of the Kardar-Parisi-Zhang Equation./
Author:	Ghosal, Promit.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2020,
Description:	193 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-11, Section: B.
Contained By:	Dissertations Abstracts International81-11B.
Subject:	Statistical physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=27956048
ISBN:	9798643175223

Time Evolution of the Kardar-Parisi-Zhang Equation.
Ghosal, Promit.

Time Evolution of the Kardar-Parisi-Zhang Equation. - Ann Arbor : ProQuest Dissertations & Theses, 2020 - 193 p.

Source: Dissertations Abstracts International, Volume: 81-11, Section: B.

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

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

The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The Kardar-Parisi-Zhang (KPZ) equation is well-known for its applications in describing various statistical mechanical models including randomly growing surfaces, directed polymers and interacting particle systems. We consider the upper and lower tail probabilities for the centered (by time=24) and scaled (according to KPZ time1/3 scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation. We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times T and demonstrates a crossover between super-exponential decay with exponent 5/2 (and leading prefactor 4/15π T1/3) for tail depth greater than T2/3 (deep tail), and exponent 3 (with leading pre-factor at least 1 12 ) for tail depth less than T2/3 (shallow tail). We also consider the case when the initial data is drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent 3 in the shallow tail to an exponent 5/2 in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent 3/2 at all depths in the tail. We study the correlation of fluctuations of the narrow wedge solution to the KPZ equation at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent 2/3 , while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent -1/3 .

ISBN: 9798643175223Subjects--Topical Terms:

536281
Statistical physics.

Time Evolution of the Kardar-Parisi-Zhang Equation.
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100 1 $a Ghosal, Promit. $3 3544918
245 1 0 $a Time Evolution of the Kardar-Parisi-Zhang Equation.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2020
300 $a 193 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-11, Section: B.
500 $a Advisor: Corwin, Ivan.
502 $a Thesis (Ph.D.)--Columbia University, 2020.
506 $a This item must not be sold to any third party vendors.
520 $a The use of the non-linear SPDEs are inevitable in both physics and applied mathematics since many of the physical phenomena in nature can be effectively modeled in random and non-linear way. The Kardar-Parisi-Zhang (KPZ) equation is well-known for its applications in describing various statistical mechanical models including randomly growing surfaces, directed polymers and interacting particle systems. We consider the upper and lower tail probabilities for the centered (by time=24) and scaled (according to KPZ time1/3 scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation. We provide the first tight bounds on the lower tail probability of the one point distribution of the KPZ equation with narrow wedge initial data. Our bounds hold for all sufficiently large times T and demonstrates a crossover between super-exponential decay with exponent 5/2 (and leading prefactor 4/15π T1/3) for tail depth greater than T2/3 (deep tail), and exponent 3 (with leading pre-factor at least 1 12 ) for tail depth less than T2/3 (shallow tail). We also consider the case when the initial data is drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent 3 in the shallow tail to an exponent 5/2 in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent 3/2 at all depths in the tail. We study the correlation of fluctuations of the narrow wedge solution to the KPZ equation at two different times. We show that when the times are close to each other, the correlation approaches one at a power-law rate with exponent 2/3 , while when the two times are remote from each other, the correlation tends to zero at a power-law rate with exponent -1/3 .
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