Fluctuations of shapes of large areas under paths of random walks

DOI10.1007/BF01191908zbMath0853.60057MaRDI QIDQ1922095

Ostap Hryniv, Roland Lvovich Dobrushin

Publication date: 16 December 1996

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

zbMATH Keywords

invariance principleIsing modelGaussian random processstatistical properties of random walks

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Large deviations (60F10) Interface problems; diffusion-limited aggregation arising in equilibrium statistical mechanics (82B24) Functional limit theorems; invariance principles (60F17)

Related Items (13)

Weakly asymmetric bridges and the KPZ equation ⋮ Surface transition in the collapsed phase of a self-interacting walk adsorbed along a hard wall ⋮ Invariance principles for integrated random walks conditioned to stay positive ⋮ Phase separation in random cluster models. III: Circuit regularity ⋮ Refined behaviour of a conditioned random walk in the large deviations regime ⋮ Interacting partially directed self-avoiding walk: a probabilistic perspective ⋮ On the centre of mass of a random walk ⋮ On the scaling limits of weakly asymmetric bridges ⋮ Some rigorous results on semiflexible polymers. I: Free and confined polymers ⋮ Tail asymptotics for the area under the excursion of a random walk with heavy-tailed increments ⋮ Local asymptotics for the area under the random walk excursion ⋮ Condensation of a self-attracting random walk ⋮ A sharp asymptotics of the partition function for the collapsed interacting partially directed self-avoiding walk

Cites Work

• On the microscopic validity of the Wulff construction and of the generalized Young equation
• Large deviations for the 2D Ising model: A lower bound without cluster expansions
• Exact large deviation bounds up to \(T_ c\) for the Ising model in two dimensions
• On the Wulff construction as a problem of equivalence of statistical ensembles
• Convex Analysis
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
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