Scaling limits of disordered systems and disorder relevance

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Francesco Caravenna , Rongfeng Sun , Nikos Zygouras This is my paper · ORCID

classification math.PRmath-phmath.MP

keywords disorderlimitsrelevancecloselycontinuumdisorderedexistencenon-trivial

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We review recent works where we have shown that disorder relevance is closely related to the existence of non-trivial, random continuum limits

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Continuum models of directed polymers on disordered diamond fractals in the critical case
math.PR 2019-08 conditional novelty 7.0 of 10

Critical continuum random polymer measures M_r are constructed on diamond fractals, and intersections of two independent paths are shown to have Hausdorff dimension zero with log-Hausdorff exponent 1.
Weak-disorder limit at criticality for directed polymers on hierarchical graphs
math-ph 2019-08 conditional novelty 7.0 of 10

The partition functions for directed polymers on diamond graphs with b=s converge in distribution to a unique limit law under a fine-tuned critical inverse-temperature scaling.