A symmetric entropy bound on the non-reconstruction regime of Markov chains on galton-watson trees.
A system of differential equations for the Airy process.
A toroidal compactification of the Fermi surface for the discrete Schrödinger operator.
A two-scale approach to logarithmic Sobolev inequalities and the hydrodynamic limit
We consider the coarse-graining of a lattice system with continuous spin variable. In the first part, two abstract results are established: sufficient conditions for a logarithmic Sobolev inequality with constants independent of the dimension (Theorem 3) and sufficient conditions for convergence to the hydrodynamic limit (Theorem 8). In the second part, we use the abstract results to treat a specific example, namely the Kawasaki dynamics with Ginzburg–Landau-type potential.
AB percolation: a brief survey
Absolutely continuous spectrum and scattering in the surface Maryland model
We study the discrete Schrödinger operator in with the surface quasi periodic potential , where . We first discuss a proof of the pure absolute continuity of the spectrum of on the interval (the spectrum of the discrete laplacian) in the case where the components of are rationally independent. Then we show that in this case the generalized eigenfunctions have the form of the “volume” waves, i.e. of the sum of the incident plane wave and reflected from the hyper-plane waves, the form...
Acceleration of material waves in Fermi accelerator.
Alcune disuguaglianze nel modello di Edwards-Anderson e in altri modelli di vetri di spin
Algebro-geometric Approach to the Yang-Baxter Equation and Related Topics
Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case
We extend the convergence method introduced in our works [8–10] for almost sure global well-posedness of Gibbs measure evolutions of the nonlinear Schrödinger (NLS) and nonlinear wave (NLW) equations on the unit ball in to the case of the three dimensional NLS. This is the first probabilistic global well-posedness result for NLS with supercritical data on the unit ball in . The initial data is taken as a Gaussian random process lying in the support of the Gibbs measure associated to the equation,...
An analysis of the effect of ghost force oscillation on quasicontinuum error
The atomistic to continuum interface for quasicontinuum energies exhibits nonzero forces under uniform strain that have been called ghost forces. In this paper, we prove for a linearization of a one-dimensional quasicontinuum energy around a uniform strain that the effect of the ghost forces on the displacement nearly cancels and has a small effect on the error away from the interface. We give optimal order error estimates that show that the quasicontinuum displacement converges to the atomistic...
An analytic formula for the Jack polynomials.
An application of Catalan numbers on Cayley tree of order 2: Single polygon counting.
An approximation of the pressure for the two-dimensional Ising model
An exactly solvable spin chain related to Hahn polynomials.
An extension of the inductive approach to the lace expansion.
An infinite level atom coupled to a heat bath.
Analysis of a Bose–Einstein Markov chain
Analysis of a force-based quasicontinuum approximation
We analyze a force-based quasicontinuum approximation to a one-dimensional system of atoms that interact by a classical atomistic potential. This force-based quasicontinuum approximation can be derived as the modification of an energy-based quasicontinuum approximation by the addition of nonconservative forces to correct nonphysical “ghost” forces that occur in the atomistic to continuum interface during constant strain. The algorithmic simplicity and consistency with the purely atomistic model at...
Analytical derivation of time spectral rigidity for thermodynamic traffic gas
We introduce an one-dimensional thermodynamical particle model which is efficient in predictions about a microscopical structure of animal/human groups. For such a model we present analytical calculations leading to formulae for time clearance distribution as well as for time spectral rigidity. Furthermore, the results obtained are reformulated in terms of vehicular traffic theory and consecutively compared to experimental traffic data.