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An informal introduction to the Parisi formula

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arxiv 2410.12364 v2 pith:I6BGZA7U submitted 2024-10-16 math.PR cond-mat.dis-nnmath-phmath.MP

Jean-Christophe Mourrat This is my paper · ORCID
classification math.PRcond-mat.dis-nnmath-phmath.MP
keywords formulaparisiinformalpartialsomeconnectiondifferentialdiscuss
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This note is an informal presentation of spin glasses and of the Parisi formula. We also discuss some models for which the Parisi formula is not well-understood, and some partial progress that relies upon a connection with partial differential equations.

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  1. Ground state energies of multipartite $p$-spin models -- partially lifted RDT view

    math.PR 2025-09 conditional novelty 6.0 of 10

    The paper uses partially lifted random duality theory to derive matching ground-state-energy bounds for spherical multipartite pure p-spin models and proves the Subag and Dartois-McKenna formulas agree exactly.

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