scholarly journals The Legendre Structure of the Parisi Formula

2016 ◽  
Vol 348 (3) ◽  
pp. 751-770 ◽  
Author(s):  
Antonio Auffinger ◽  
Wei-Kuo Chen
Keyword(s):  
Parisi Formula

scholarly journals Random assignment and shortest path problems

2006 ◽  
Vol DMTCS Proceedings vol. AG,... (Proceedings) ◽  
Author(s):  
Johan Wästlund
Keyword(s):  
Limit Theorem ◽  
Shortest Path ◽  
Complete Graph ◽  
Assignment Problem ◽  
Shortest Path Problem ◽  
Random Assignment ◽  
Shortest Path Problems ◽  
Parisi Formula ◽  
International Audience ◽  
Random Assignment Problem

International audience We explore a similarity between the $n$ by $n$ random assignment problem and the random shortest path problem on the complete graph on $n+1$ vertices. This similarity is a consequence of the proof of the Parisi formula for the assignment problem given by C. Nair, B. Prabhakar and M. Sharma in 2003. We give direct proofs of the analogs for the shortest path problem of some results established by D. Aldous in connection with his $\zeta (2)$ limit theorem for the assignment problem.

scholarly journals FREE ENERGY IN THE GENERALIZED SHERRINGTON–KIRKPATRICK MEAN FIELD MODEL

2005 ◽  
Vol 17 (07) ◽  
pp. 793-857 ◽  
Author(s):  
DMITRY PANCHENKO
Keyword(s):  
Free Energy ◽  
Real Line ◽  
Prior Distribution ◽  
Field Model ◽  
Mean Field ◽  
Rigorous Proof ◽  
Bounded Subset ◽  
Mean Field Model ◽  
The Real ◽  
Parisi Formula

In [11], Talagrand gave a rigorous proof of the Parisi formula in the classical Sherrington–Kirkpatrick (SK) model. In this paper, we build upon the methodology developed in [11] and extend Talagrand's result to the class of SK type models in which the spins have arbitrary prior distribution on a bounded subset of the real line.

scholarly journals The Parisi formula for mixed $p$-spin models

2014 ◽  
Vol 42 (3) ◽  
pp. 946-958 ◽  
Author(s):  
Dmitry Panchenko
Keyword(s):  
Spin Models ◽  
Parisi Formula

scholarly journals Parisi formula for the ground state energy in the mixed $p$-spin model

2017 ◽  
Vol 45 (6B) ◽  
pp. 4617-4631 ◽  
Author(s):  
Antonio Auffinger ◽  
Wei-Kuo Chen
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Spin Model ◽  
Parisi Formula
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