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arxiv: math-ph/0510038 · v1 · submitted 2005-10-10 · 🧮 math-ph · math.MP· math.PR

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Random matrices and determinantal processes

Kurt Johansson
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classification 🧮 math-ph math.MPmath.PR
keywords randomdeterminantalprocessesgrowthmatricesmatrixrecentrelation
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We survey recent results on determinantal processes, random growth, random tilings and their relation to random matrix theory.

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  1. A transition in the hole probability at finite temperature for free fermions in $d$ dimensions

    cond-mat.stat-mech 2026-05 conditional novelty 8.0

    Free fermions in d dimensions have a hole probability that scales as exp[-(k_F R)^{d+1} Φ_d(u)] with a transition of order 3/2(d+1) in Φ_d at the universal point u_c=2/π, computed exactly via Coulomb gas mapping.