Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calculable baseline for dynamical heterogeneity in glassy systems.
Statics and dynamics of infinite-dimensional liquids and glasses: a parallel, compact derivation
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abstract
We provide a compact derivation of the static and dynamic equations for infinite-dimensional particle systems in the liquid and glass phases. The static derivation is based on the introduction of an "auxiliary" disorder and the use of the replica method. The dynamic derivation is based on the general analogy between replicas and the supersymmetric formulation of dynamics. We show that static and dynamic results are consistent, and follow the Random First Order Transition scenario of mean field disordered glassy systems.
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cond-mat.stat-mech 1years
2026 1verdicts
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A Shared Observation Shields Collective Fluctuations while Preserving Local Independence
Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calculable baseline for dynamical heterogeneity in glassy systems.