Variational Approximation Methods for Elliptic PDEs

2016 ◽  
pp. 145-166
Author(s):  
Hervé Le Dret ◽  
Brigitte Lucquin
Keyword(s):  
Variational Approximation ◽  
Elliptic Pdes ◽  
Approximation Methods

scholarly journals ENTROPY OF OPERATOR-VALUED RANDOM VARIABLES: A VARIATIONAL PRINCIPLE FOR LARGE N MATRIX MODELS

2002 ◽  
Vol 17 (18) ◽  
pp. 2413-2444 ◽  
Author(s):  
L. AKANT ◽  
G. S. KRISHNASWAMI ◽  
S. G. RAJEEV
Keyword(s):  
Matrix Models ◽  
Classical Theory ◽  
Reasonable Agreement ◽  
Probability Distributions ◽  
Equations Of Motion ◽  
Action Principle ◽  
Variational Approximation ◽  
Approximation Methods ◽  
Noncommutative Probability ◽  
Large N

We show that, in 't Hooft's large N limit, matrix models can be formulated as a classical theory whose equations of motion are the factorized Schwinger–Dyson equations. We discover an action principle for this classical theory. This action contains a universal term describing the entropy of the noncommutative probability distributions. We show that this entropy is a nontrivial one-cocycle of the noncommutative analog of the diffeomorphism group and derive an explicit formula for it. The action principle allows us to solve matrix models using novel variational approximation methods; in the simple cases where comparisons with other methods are possible, we get reasonable agreement.

Variational Approximation Methods

2017 ◽  
pp. 259-270
Author(s):  
Frank Rijmen ◽  
Minjeong Jeon ◽  
Sophia Rabe-Hesketh
Keyword(s):  
Variational Approximation ◽  
Approximation Methods

Manifolds in random media: beyond the variational approximation

1994 ◽  
Vol 4 (1) ◽  
pp. 87-100 ◽  
Author(s):  
Yadin Y. Goldschmidt
Keyword(s):  
Random Media ◽  
Variational Approximation
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