Wetting of gradient fields: pathwise estimates

Velenik, Yvan

doi:10.1007/s00440-007-0130-x

Probab. Theory Relat. Fields

2008

DOI: 10.1007/s00440-007-0130-x

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Wetting of gradient fields: pathwise estimates

Yvan Velenik

Abstract: We consider the wetting transition in the framework of an effective interface model of gradient type, in dimension 2 and higher. We prove pathwise estimates showing that the interface is localized in the whole thermodynamically-defined partial wetting regime considered in earlier works. Moreover, we study how the interface delocalizes as the wetting transition is approached. Our main tool is reflection positivity in the form of the chessboard estimate.

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Cited by 3 publications

(1 citation statement)

References 15 publications

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“…The FS distribution has also appeared in other systems [36,[52][53][54][55]. This is indicative of a universality class.…”

mentioning

confidence: 68%

Airy distribution: Experiment, large deviations, and additional statistics

Agranov

Zilber

Smith

et al. 2020

Phys. Rev. Research

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The Airy distribution (AD) describes the probability distribution of the area under a Brownian excursion. The AD is prominent in several areas of physics, mathematics and computer science. Here we use a dilute colloidal system to directly measure, for the first time, the AD in experiment. We also show how two different techniques of theory of large deviations -the Donsker-Varadhan formalism and the optimal fluctuation method -manifest themselves in the AD. We advance the theory of the AD by calculating, at large and small areas, the position distribution of a Brownian excursion conditioned on a given area. For large areas, we uncover two singularities in the large deviation function, which can be interpreted as dynamical phase transitions of third order. For small areas the position distribution coincides with the Ferrari-Spohn distribution, which has previously appeared in other problems, and we identify the reason for this coincidence.

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“…The FS distribution has also appeared in other systems [36,[52][53][54][55]. This is indicative of a universality class.…”

mentioning

confidence: 68%

Airy distribution: Experiment, large deviations, and additional statistics

Agranov

Zilber

Smith

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

Entropic Repulsion of the Massless Field with a Class of Self-potentials

Sakagawa

2009

J Stat Phys

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Disorder and wetting transition: The pinned harmonic crystal in dimension three or larger

Giacomin¹,

Lacoin²

2018

Ann. Appl. Probab.

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We consider the Lattice Gaussian free field in d + 1 dimensions, d = 3 or larger, on a large box (linear size N ) with boundary conditions zero. On this field two potentials are acting: one, that models the presence of a wall, penalizes the field when it enters the lower half space and one, the pinning potential, that rewards visits to the proximity of the wall. The wall can be soft, i.e. the field has a finite penalty to enter the lower half plane, or hard when the penalty is infinite. In general the pinning potential is disordered and it gives on average a reward h ∈ R (a negative reward is a penalty): the energetic contribution when the field at site x visits the pinning region is βωx + h, {ωx} x∈Z d are IID centered and exponentially integrable random variables of unit variance and β ≥ 0. In [3] it is shown that, when β = 0 (that is, in the non disordered model), a delocalization-localization transition happens at h = 0, in particular the free energy of the system is zero for h ≤ 0 and positive for h > 0. We show that, for β = 0, the transition happens at h = hc(β) := − log E exp(βωx) and we find the precise asymptotic behavior of the logarithm of the free energy density of the system when h ց hc(β).In particular, we show that the transition is of infinite order in the sense that the free energy is smaller than any power of h − hc(β) in the neighborhood of the critical point and that disorder does not modify at all the nature of the transition. We also provide results on the behavior of the paths of the random field in the limit N → ∞.

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Wetting of gradient fields: pathwise estimates

Cited by 3 publications

References 15 publications

Airy distribution: Experiment, large deviations, and additional statistics

Airy distribution: Experiment, large deviations, and additional statistics

Entropic Repulsion of the Massless Field with a Class of Self-potentials

Disorder and wetting transition: The pinned harmonic crystal in dimension three or larger

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