1,721,060 research outputs found
Exact Results on the First Hitting via Conditional Strong Quasi-Stationary Times and Applications to Metastability
No full textIn the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set G are obtained. A new notion of “conditional strong quasi stationary time” is introduced to describe the local relaxation time. This time is defined via a generalization of the strong stationary time. Rarity of the target set G is not required and the initial distribution can be completely general. The results clarify the the role played by the initial distribution on the exponential law; they are used to give a general notion of metastability and to discuss the relation between the exponential distribution of the first hitting time and metastability
SMALL RANDOM PERTURBATIONS OF DYNAMICAL-SYSTEMS - EXPONENTIAL LOSS OF MEMORY OF THE INITIAL CONDITION
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REMARK ON THE ABSENCE OF ABSOLUTELY CONTINUOUS-SPECTRUM FOR D-DIMENSIONAL SCHRODINGER-OPERATORS WITH RANDOM POTENTIAL FOR LARGE DISORDER OR LOW-ENERGY
No full textAnisotropy effects in nucleation for conservative dynamics
No full textWe analyze metastability and nucleation in the context of a local version of the Kawasaki dynamics for the two-dimensional it anisotropic Ising lattice gas at very low temperature. Let Lambda subset of Z(2) be a sufficiently large finite box. Particles perform simple exclusion on L, but when they occupy neighboring sites they feel a binding energy -U-1< 0 in the horizontal direction and U-2< 0 in the vertical direction; we assume U-1>= U-2. Along each bond touching the boundary of L from the outside, particles are created with rate rho=e(-Delta beta) and are annihilated with rate 1, where beta is the inverse temperature and Delta > 0 is an activity parameter. Thus, the boundary of L plays the role of an infinite gas reservoir with density rho. We take Delta is an element of (U-1,U-1+U-2) where the totally empty (full) configuration can be naturally associated to metastability (stability). We investigate how the transition from empty to full takes place under the dynamics. In particular, we identify the size and some characteristics of the shape of the it critical droplet/ and the time of its creation in the limit as btoinfty. We observe very different behavior in the weakly or strongly anisotropic case. In both case we find that Wulff shape is not relevant for the nucleation pattern
SMALL RANDOM PERTURBATIONS OF FINITE-DIMENSIONAL AND INFINITE-DIMENSIONAL DYNAMICAL-SYSTEMS - UNPREDICTABILITY OF EXIT TIMES
No full textMETASTABILITY AND EXPONENTIAL APPROACH TO EQUILIBRIUM FOR LOW-TEMPERATURE STOCHASTIC ISING-MODELS
No full textON THE SWENDSEN-WANG DYNAMICS .2. CRITICAL DROPLETS AND HOMOGENEOUS NUCLEATION AT LOW-TEMPERATURE FOR THE 2-DIMENSIONAL ISING-MODEL
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