Random Matrices and complexity of Spin Glasses

M. Plancherel and W. Rotach, Sur les valeurs asymptotiques des polynomes d’Hermite , Comment. Math. Helv. 1

1929

Earlier work this paper cites.

J. Kurchan and L. Laloux, Phase space geometry and slow dynamics , J. Phys. A: Math. Gen. 29

1948

Earlier work this paper cites.

Gábor Szegő, Orthogonal polynomials , fourth ed., American Mathematical Society, Providence, R.I., 1981, American Mathematical Society, Colloquium Publications, Vol. XXIII

1981

Earlier work this paper cites.

M. L. Mehta, Random matrices , second ed., Academic Press Inc., Boston, MA, 1991. MR MR1083764 (92f:82002)

1991

Earlier work this paper cites.

J. Kurchan, G. Parisi, and M. A. Virasoro, Barriers and metastable states as saddle points in the replica approach , J.Phys. I France 3

1993

Earlier work this paper cites.

A. Crisanti and H-J. Sommers, Thouless-Anderson-Palmer approach to the spherical p p -spin spin glass model , J. Phys. I France 5

1995

Earlier work this paper cites.

G. Ben Arous and A. Guionnet, Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy , Probab. Theory Related Fields 108

1997

Earlier work this paper cites.

Amir Dembo and Ofer Zeitouni, Large deviations techniques and applications , second ed., Applications of Mathematics, vol. 38, Springer-Verlag, New York, 1998. MR MR1619036 (99d:60030)

1998

Cited alongside, same era.

P. Deift, T. Kriecherbauer, K. T-R McLaughlin, S. Venakides, and X. Zhou, Strong asymptotics of orthogonal polynomials with respect to exponential weights , Comm. Pure Appl. Math. 52

1999

Cited alongside, same era.

G. Ben Arous, A. Dembo, and A. Guionnet, Aging of spherical spin glasses , Probab. Theory Related Fields 120

2001

Cited alongside, same era.

A. Crisanti, L. Leuzzi, and T. Rizzo, The complexity of the spherical p p -spin spin glass model, revisited , The European Physical Journal B - Condensed Matter and Complex Systems 36

2003

Cited alongside, same era.

Yan V. Fyodorov, Complexity of random energy landscapes, glass transition and absolute value of spectral determinant of random matrices , Physical Rev. Let. 92

Robert J. Adler and Jonathan E. Taylor, Random fields and geometry , Springer Monographs in Mathematics, Springer, New York, 2007. MR MR2319516

2007

Later among the works it cites.

Percy Deift and Dimitri Gioev, Universality in random matrix theory for orthogonal and symplectic ensembles , Int. Math. Res. Pap. IMRP 2007

2007

Later among the works it cites.

Yan V. Fyodorov and Ian Williams, Replica symmetry breaking condition exposed by random matrix calculation of landscape complexity , J. Stat. Phys. 129

2007

Later among the works it cites.

Dmitry Panchenko and Michel Talagrand, On the overlap in the multiple spherical SK models , Ann. Probab. 35

2007

Later among the works it cites.

Jean-Marc Azaïs and Mario Wschebor, Level sets and extrema of random processes and fields , John Wiley & Sons Inc., Hoboken, NJ, 2009. MR MR2478201

2009