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A Mixed Formulation of the Monge-Kantorovich Equations

John W. Barrett, Leonid Prigozhin (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We introduce and analyse a mixed formulation of the Monge-Kantorovich equations, which express optimality conditions for the mass transportation problem with cost proportional to distance. Furthermore, we introduce and analyse the finite element approximation of this formulation using the lowest order Raviart-Thomas element. Finally, we present some numerical experiments, where both the optimal transport density and the associated Kantorovich potential are computed for a coupling problem and problems...

Disorder relevance at marginality and critical point shift

Giambattista Giacomin, Hubert Lacoin, Fabio Lucio Toninelli (2011)

Annales de l'I.H.P. Probabilités et statistiques

Recently the renormalization group predictions on the effect of disorder on pinning models have been put on mathematical grounds. The picture is particularly complete if the disorder is relevant or irrelevant in the Harris criterion sense: the question addressed is whether quenched disorder leads to a critical behavior which is different from the one observed in the pure, i.e. annealed, system. The Harris criterion prediction is based on the sign of the specific heat exponent of the pure system,...

Duality of Schramm-Loewner evolutions

Julien Dubédat (2009)

Annales scientifiques de l'École Normale Supérieure

In this note, we prove a version of the conjectured duality for Schramm-Loewner Evolutions, by establishing exact identities in distribution between some boundary arcs of chordal SLE κ , κ > 4 , and appropriate versions of SLE κ ^ , κ ^ = 16 / κ .

Hierarchical pinning model in correlated random environment

Quentin Berger, Fabio Lucio Toninelli (2013)

Annales de l'I.H.P. Probabilités et statistiques

We consider the hierarchical disordered pinning model studied in (J. Statist. Phys.66 (1992) 1189–1213), which exhibits a localization/delocalization phase transition. In the case where the disorder is i.i.d. (independent and identically distributed), the question of relevance/irrelevance of disorder (i.e. whether disorder changes or not the critical properties with respect to the homogeneous case) is by now mathematically rather well understood (Probab. Theory Related Fields148 (2010) 159–175,...

The scaling limits of a heavy tailed Markov renewal process

Julien Sohier (2013)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we consider heavy tailed Markov renewal processes and we prove that, suitably renormalised, they converge in law towards the α -stable regenerative set. We then apply these results to the strip wetting model which is a random walk S constrained above a wall and rewarded or penalized when it hits the strip [ 0 , ∞ ) × [ 0 , a ] where a is a given positive number. The convergence result that we establish allows to characterize the scaling limit of this process at criticality.

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