Cahn-Hilliard equation with terms of lower order and non-constant mobility.
C*-algebraic generalization of relative entropy and entropy
Canonical distributions and phase transitions
Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may be used to exhibit...
Capacity bounds for the CDMA system and a neural network: a moderate deviations approach
We study two systems that are based on sums of weakly dependent Bernoulli random variables that take values ± 1 with equal probabilities. We show that already one step of the so-called soft decision parallel interference cancellation, used in the third generation of mobile telecommunication CDMA, is able to considerably increase the number of users such a system can host. We also consider a variant of the well-known Hopfield model of neural networks. We show that this variant proposed by Amari...
Cascaded Channels and the Equivocation Inequality.
Cavity method in the spherical SK model
We develop a cavity method for the spherical Sherrington–Kirkpatrick model at high temperature and small external field. As one application we compute the limit of the covariance matrix for fluctuations of the overlap and magnetization.
Central limit theorems for the Potts model.
Chaotic hypothesis and universal large deviations properties.
Choosing Hydrodynamic Fields
Continuum mechanics (e.g., hydrodynamics, elasticity theory) is based on the assumption that a small set of fields provides a closed description on large space and time scales. Conditions governing the choice for these fields are discussed in the context of granular fluids and multi-component fluids. In the first case, the relevance of temperature or energy as a hydrodynamic field is justified. For mixtures, the use of a total temperature and single...
Classification of subfactors: the reduction to commuting squares.
Clusters in middle-phase percolation on hyperbolic plane
I consider p-Bernoulli bond percolation on transitive, nonamenable, planar graphs with one end and on their duals. It is known from [BS01] that in such a graph G we have three essential phases of percolation, i.e. , where is the critical probability and -the unification probability. I prove that in the middle phase a.s. all the ends of all the infinite clusters have one-point boundaries in ∂ℍ². This result is similar to some results in [Lal].
Coarse graining, fractional moments and the critical slope of random copolymers.
Coarse-graining schemes and a posteriori error estimates for stochastic lattice systems
The primary objective of this work is to develop coarse-graining schemes for stochastic many-body microscopic models and quantify their effectiveness in terms of a priori and a posteriori error analysis. In this paper we focus on stochastic lattice systems of interacting particles at equilibrium. The proposed algorithms are derived from an initial coarse-grained approximation that is directly computable by Monte Carlo simulations, and the corresponding numerical error is calculated using the...
Coexistence probability in the last passage percolation model is
A competition model on between three clusters and governed by directed last passage percolation is considered. We prove that coexistence, i.e. the three clusters are simultaneously unbounded, occurs with probability . When this happens, we also prove that the central cluster almost surely has a positive density on . Our results rely on three couplings, allowing to link the competition interfaces (which represent the borderlines between the clusters) to some particles in the multi-TASEP, and...
Combinatorial analysis of magnetic configurations.
Combinatorics and cluster expansions.
Combinatorics of the three-parameter PASEP partition function.
Combinatorics of tripartite boundary connections for trees and dimers.
Combined analysis of two- and three-particle correlations in -Bose gas model.
Combining stochastic and deterministic approaches within high efficiency molecular simulations
Generalized Shadow Hybrid Monte Carlo (GSHMC) is a method for molecular simulations that rigorously alternates Monte Carlo sampling from a canonical ensemble with integration of trajectories using Molecular Dynamics (MD). While conventional hybrid Monte Carlo methods completely re-sample particle’s velocities between MD trajectories, our method suggests a partial velocity update procedure which keeps a part of the dynamic information throughout the simulation. We use shadow (modified) Hamiltonians,...