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Random matrices, complexity of spin ...

Auffinger, Antonio.

Random matrices, complexity of spin glasses and heavy tailed processes.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Random matrices, complexity of spin glasses and heavy tailed processes.
Author:	Auffinger, Antonio.
Description:	243 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-10, Section: B, page: 6022.
Notes:	Adviser: Gerard Ben Arous.
Contained By:	Dissertation Abstracts International72-10B.
Subject:	Applied Mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3466846
ISBN:	9781124807355

Random matrices, complexity of spin glasses and heavy tailed processes.
Auffinger, Antonio.

Random matrices, complexity of spin glasses and heavy tailed processes. - 243 p.

Source: Dissertation Abstracts International, Volume: 72-10, Section: B, page: 6022.

Thesis (Ph.D.)--New York University, 2011.

In the first part of this thesis we introduce a new identity relating critical values of random Hamiltonians in certain compact manifolds to eigenvalues of random matrix ensembles. This identity allows us identify the location of the ground state energy and obtain an explicit formula for the asymptotic complexity of the number of critical points of finite and diverging index at any level of energy. We show that two possible scenarios for the bottom energy landscape emerge. This picture is consistent with a transition from a glass to spin glass system.

ISBN: 9781124807355Subjects--Topical Terms:

530992
Applied Mathematics.

Random matrices, complexity of spin glasses and heavy tailed processes.
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100 1 $a Auffinger, Antonio. $3 603181
245 1 0 $a Random matrices, complexity of spin glasses and heavy tailed processes.
300 $a 243 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-10, Section: B, page: 6022.
500 $a Adviser: Gerard Ben Arous.
502 $a Thesis (Ph.D.)--New York University, 2011.
520 $a In the first part of this thesis we introduce a new identity relating critical values of random Hamiltonians in certain compact manifolds to eigenvalues of random matrix ensembles. This identity allows us identify the location of the ground state energy and obtain an explicit formula for the asymptotic complexity of the number of critical points of finite and diverging index at any level of energy. We show that two possible scenarios for the bottom energy landscape emerge. This picture is consistent with a transition from a glass to spin glass system.
520 $a In the second part, we establish the limit laws for largest eigenvalues of Wigner and Sample Covariance matrices when the entries are heavy tailed with less than four moments. We then study a model of Directed Polymer in a heavy tailed Random Environment proving a scaling limit law for the polymer measure.
590 $a School code: 0146.
650 4 $a Applied Mathematics. $3 530992
650 4 $a Mathematics. $3 184409
650 4 $a Chemistry, Polymer. $3 227045
650 4 $a Engineering, Materials Science. $3 226940
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690 $a 0405
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710 2 $a New York University. $b Mathematics. $3 603182
773 0 $t Dissertation Abstracts International $g 72-10B.
790 1 0 $a Arous, Gerard Ben, $e advisor
790 1 0 $a Chatterjee, Sourav $e committee member
790 1 0 $a Deift, Percy $e committee member
790 1 0 $a Newman, Charles M. $e committee member
790 1 0 $a Varadhan, S.R.S. $e committee member
790 $a 0146
791 $a Ph.D.
792 $a 2011
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3466846