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Tightness of the maximum of Ginzburg-Landau fields

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arxiv 2403.11500 v1 pith:YCLAPIRQ submitted 2024-03-18 math.PR math-phmath.MP

Florian Schweiger , Wei Wu , Ofer Zeitouni This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords ginzburg-landaumaximumboxescenteredcenteringconditionconsiderconvexity
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abstract

We consider the discrete Ginzburg-Landau field with potential satisfying a uniform convexity condition, in the critical dimension $d=2$, and prove that its maximum over boxes of sidelength $N$, centered by an explicit $N$-dependent centering, is tight.

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  1. Extremal process of the local time of simple random walk on a regular tree

    math.PR 2025-06 conditional novelty 8.0 of 10

    The extremal process of centered square-root local time on the leaves of a regular tree converges to a decorated Poisson point process with the same cluster law as the Gaussian Free Field.

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