Two Random Interfaces of Statistical Mechanics Models
نویسنده
چکیده
We consider the limiting statistical properties of fluctuations of statistical mechanics models. The two random interfaces of one-dimensional statistical physics models is modeled and investigated in the present paper. The two random interfaces are constructed by assuming that there is a specified value of the large area in the intermediate region of the two random interfaces, and the two random interfaces have fixed endpoints. When the inverse temperature is large enough, we show that the limiting distributions of the two random interfaces of the model convergence to a Gaussian distribution. Keywords—Two random interfaces, Gaussian distribution, probability measure, fluctuation.
منابع مشابه
Quenched noise and over-active sites in sandpile dynamics
– The dynamics of sandpile models are mapped to discrete interface equations. We study in detail the Bak-Tang-Wiesenfeld model, a stochastic model with random thresholds, and the Manna model. These sandpile models are, respectively, discretizations of the Edwards-Wilkinson equation with columnar, point-like and correlated quenched noise, with the constraint that the interface velocity is either...
متن کاملA pr 2 00 7 Continuous interfaces with disorder : Even strong pinning is too weak in 2 dimensions
We consider statistical mechanics models of continuous height effective interfaces in the presence of a delta-pinning of strength ε at height zero. There is a detailed mathematical understanding of the depinning transition in 2 dimensions without disorder. Then the variance of the interface height w.r.t. the Gibbs measure stays bounded uniformly in the volume for ε > 0 and diverges like | log ε...
متن کاملMultiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales
A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conform...
متن کاملModelling of Random Geometrical Imperfections and Reliability Calculations for Thin Cylindrical Shell Subjected to Lateral Pressure
It is well known that it is very difficult to manufacture perfect thin cylindrical shell. Initial geometrical imperfections existing in the shell structure is one of the main determining factor for load bearing capacity of thin cylindrical shell under uniform lateral pressure. As these imperfections are random, the strength of same size cylindrical shell will also random and a statistical metho...
متن کاملDipolar Sles
We present basic properties of Dipolar SLEs, a new version of stochastic Loewner evolutions (SLE) in which the critical interfaces end randomly on an interval of the boundary of a planar domain. We present a general argument explaining why correlation functions of models of statistical mechanics are expected to be martingales and we give a relation between dipolar SLEs and CFTs. We compute SLE ...
متن کامل