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Non-intersecting Random Processes an...

ProQuest Information and Learning Co.

Non-intersecting Random Processes and Multi-layer Random Polymers.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Non-intersecting Random Processes and Multi-layer Random Polymers./
Author:	Nica, Mihai.
Description:	1 online resource (308 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.
Contained By:	Dissertation Abstracts International79-01B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9780355128048

Non-intersecting Random Processes and Multi-layer Random Polymers.
Nica, Mihai.

Non-intersecting Random Processes and Multi-layer Random Polymers. - 1 online resource (308 pages)

Source: Dissertation Abstracts International, Volume: 79-01(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

This thesis deals with understanding multi-layer generalizations of last passage percolation and directed random polymer models. These models are constructed from non-intersecting random processes in a random environment.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355128048Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Non-intersecting Random Processes and Multi-layer Random Polymers.
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100 1 $a Nica, Mihai. $3 1114547
245 1 0 $a Non-intersecting Random Processes and Multi-layer Random Polymers.
264 0 $c 2017
300 $a 1 online resource (308 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: 79-01(E), Section: B.
500 $a Adviser: Gerard Ben Arous.
502 $a Thesis (Ph.D.) $c New York University $d 2017.
504 $a Includes bibliographical references
520 $a This thesis deals with understanding multi-layer generalizations of last passage percolation and directed random polymer models. These models are constructed from non-intersecting random processes in a random environment.
520 $a In the first part of the thesis, an interacting particle system in discrete time with deterministic evolution but random initial condition is studied. An unexpected non-Gaussian behavior is found in this model when the number of particles and holes in the initial condition are nearly equal. The model is related to a last passage percolation problem in a thin strip.
520 $a Next, a generalization of last passage percolation in an environment of Poisson points is studied. It is shown that this system can be understood in terms of certain Young tableaux which are decorated with additional information. The law of this process is characterized in terms of Schur processes and also in terms of non-intersecting Poisson paths. This allows computation of asymptotic properties of the model. For example, convergence to the Airy process is proven.
520 $a Finally, directed random polymers in a random environment are studied. The intermediate disorder regime is a scaling limit for disordered systems where the temperature is critically scaled as the size of the system grows to infinity. It is shown that multiple directed random polymers, which start and end grouped together, have a universal limit in this intermediate disorder scaling. This result is proven both for a wide class of discrete random polymer models and for a certain semi-discrete polymer model. The universal limiting object is shown to be a multi-layer generalization of the Kardar-Parisi-Zhang (KPZ) equation known as the KPZ line ensemble.
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 Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a New York University. $b Mathematics. $3 1180487
773 0 $t Dissertation Abstracts International $g 79-01B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10260599 $z click for full text (PQDT)

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