Convergence of critical oriented percolation to super-brownian motion above dimensions
Convergence of lattice trees to super-Brownian motion above the critical dimension.
Convergence of minimax structures and continuation of critical points for singularly perturbed systems
In the recent literature, the phenomenon of phase separation for binary mixtures of Bose–Einstein condensates can be understood, from a mathematical point of view, as governed by the asymptotic limit of the stationary Gross–Pitaevskii system , as the interspecies scattering length goes to . For this system we consider the associated energy functionals , with -mass constraints, which limit (as ) is strongly irregular. For such functionals, we construct multiple critical points via a common...
Convergence results and sharp estimates for the voter model interfaces.
Coordinate Bethe ansatz for spin XXX model.
Copolymer at selective interfaces and pinning potentials : weak coupling limits
We consider a simple random walk of length N, denoted by (Si)i∈{1, …, N}, and we define (wi)i≥1 a sequence of centered i.i.d. random variables. For K∈ℕ we define ((γi−K, …, γiK))i≥1 an i.i.d sequence of random vectors. We set β∈ℝ, λ≥0 and h≥0, and transform the measure on the set of random walk trajectories with the hamiltonian λ∑i=1N(wi+h)sign(Si)+β∑j=−KK∑i=1Nγij1{Si=j}. This transformed path measure describes an hydrophobic(philic) copolymer interacting with a layer of width 2K around an interface...
Corrector results for a parabolic problem with a memory effect
The aim of this paper is to provide the correctors associated to the homogenization of a parabolic problem describing the heat transfer. The results here complete the earlier study in [Jose, Rev. Roumaine Math. Pures Appl.54 (2009) 189–222] on the asymptotic behaviour of a problem in a domain with two components separated by an ε-periodic interface. The physical model established in [Carslaw and Jaeger, The Clarendon Press, Oxford (1947)] prescribes on the interface the condition that the flux...
Correlation function and simplified TBA equations for XXZ chain.
Correlation lengths for random polymer models and for some renewal sequences.
Critical path analysis for continuum percolation
Critical percolation on certain nonunimodular graphs.
Cycle structure of percolation on high-dimensional tori
In the past years, many properties of the largest connected components of critical percolation on the high-dimensional torus, such as their sizes and diameter, have been established. The order of magnitude of these quantities equals the one for percolation on the complete graph or Erdős–Rényi random graph, raising the question whether the scaling limits of the largest connected components, as identified by Aldous (1997), are also equal. In this paper, we investigate the cycle structureof the largest...
Cyclic Cohomology, Supersymmetry and KMS States The KMS States as Generalized Elliptic Operators
Decay of covariances, uniqueness of ergodic component and scaling limit for a class of systems with non-convex potential
We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for -Gibbs measures, the decay of covariances, the scaling limit and the strict convexity of the surface tension.
Decay of spatial correlations in thermal states
Decimation on the Two Dimensionnal Ising Model : Non Gibbsianness at Low Temperature. Almost Gibbsianness or Weak Gibbsianness ?
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes
This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...
Dependence of the temperature of phase transitions on the size of the domain.
Depinning of a polymer in a multi-interface medium.
Derivation of a discrete Enskog equation from the dynamics of particles.