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In this short note, we present a theorem concerning certain "additive structure" for the level sets of non-degenerate Gaussian fields, which yields the multiple valley phenomenon for extremal fields with exponentially many valleys.
Extremal properties of half-spaces for spherically invariant measures
V. N. Sudakov and B. S. Tsirel ′ · 1974
Earlier work this paper cites.
The Brunn-Minkowski inequality in Gauss space
C. Borell · 1975
Earlier work this paper cites.
Local times and quantum fields
E. B. Dynkin · 1984
Earlier work this paper cites.
Threshold limits for cover times
D. J. Aldous · 1991
Earlier work this paper cites.
Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
M. B. Marcus and J. Rosen · 1992
Cited alongside, same era.
A Ray-Knight theorem for symmetric Markov processes
N. Eisenbaum, H. Kaspi, M. B. Marcus, J. Rosen, and Z. Shi · 2000
Cited alongside, same era.
Entropic repulsion and the maximum of the two-dimensional harmonic crystal
E. Bolthausen, J.-D. Deuschel, and G. Giacomin · 2001
Cited alongside, same era.
Chaos, concentration, and multiple valleys
S. Chatterjee
Cited in the paper.
Disorder chaos and multiple valleys in spin glasses
S. Chatterjee
Cited in the paper.
Asymptotics of cover times via gaussian free fields: bounded-degree graphs and general trees
J. Ding
Cited in the paper.
The Concentration of Measure Phenomenon
M. Ledoux · 2001
Later among the works it cites.
Extremes of the discrete two-dimensional Gaussian free field
O. Daviaud · 2006
Later among the works it cites.
Cover times, blanket times, and majorizing measures
J. Ding, J. R. Lee, and Y. Peres · 2012
Later among the works it cites.
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