Fetching the paper…
Reading the bibliography…
We analyze the landscape of general smooth Gaussian functions on the sphere in dimension $N$, when $N$ is large.
Plancherel, M.M. andRotach, W.W. (1929). Sur les valeurs asymptotiques des polynomes d’Hermite H n ( x ) = ( − I ) n e x 2 / 2 d n d x n ( e − x 2 2 ) H_{n}(x)=(-I)^{n}e^{{{x^{2}}}/{2}}\frac{{d^{n}}}{{dx^{n}}}({e^{-\frac{{x^{2}}}{2}}}) . Comment. Math. Helv. 1 227–254
1929
Earlier work this paper cites.
Schoenberg, I. J.I. J. (1942). Positive definite functions on spheres. Duke Math. J. 9 96–108
1942
Earlier work this paper cites.
1971
Earlier work this paper cites.
Crisanti, A.A. andSommers, H. J.H. J. (1995). On the tap approach to the spherical p p -spin sg model. J. Phys. I France 5 805–813
1995
Earlier work this paper cites.
Ben Arous, G.G. andGuionnet, A.A. (1997). Large deviations for Wigner’s law and Voiculescu’s non-commutative entropy. Probab. Theory Related Fields 108 517–542
1997
Earlier work this paper cites.
Dembo, AmirA. andZeitouni, OferO. (1998). Large Deviations Techniques and Applications, 2nd ed. Applications of Mathematics (New York) 38. Springer, New York
1998
Earlier work this paper cites.
Taylor, Jonathan E.J. E. andAdler, Robert J.R. J. (2003). Euler characteristics for Gaussian fields on manifolds. Ann. Probab. 31 533–563
2003
Cited alongside, same era.
Crisanti, A.A. andLeuzzi, L.L. (2004). Spherical 2 + p 2+p spin-glass model: An exactly solvable model for glass to spin-glass transition. Phys. Rev. Lett. 93 21203–21207
2004
Cited alongside, same era.
Fyodorov, Yan V.Y. V. (2004). Complexity of random energy landscapes, glass transition, and absolute value of the spectral determinant of random matrices. Phys. Rev. Lett. 92 240601, 4
2004
Cited alongside, same era.
Taylor, JonathanJ., Takemura, AkimichiA. andAdler, Robert J.R. J. (2005). Validity of the expected Euler characteristic heuristic. Ann. Probab. 33 1362–1396
2005
Cited alongside, same era.
Talagrand, MichelM. (2006). The Parisi formula. Ann. of Math. (2) 163 221–263
2006
Adler, Robert J.R. J. andTaylor, Jonathan E.J. E. (2007). Random Fields and Geometry. Springer, New York
2007
Later among the works it cites.
Fyodorov, Yan V.Y. V. andWilliams, IanI. (2007). Replica symmetry breaking condition exposed by random matrix calculation of landscape complexity. J. Stat. Phys. 129 1081–1116
2007
Later among the works it cites.
Azaïs, Jean-MarcJ.-M. andWschebor, MarioM. (2009). Level Sets and Extrema of Random Processes and Fields. Wiley, Hoboken, NJ
2009
Later among the works it cites.
Bleistein, NormanN. andHandelsman, Richard A.R. A. (2010). Asymptotic Expansions of Integrals, 2nd ed. Dover, New York
2010
Later among the works it cites.
Auffinger, AntonioA., Ben Arous, GérardG. andČerný, JiříJ. (2013). Random matrices and complexity of spin glasses. Comm. Pure Appl. Math. 66 165–201
2013
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.