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Mean-field critical behaviour for percolation in high dimensions
AbstractThe triangle condition for percolation states that $$\sum\limits_{x,y} {\tau (0,x)\tau (0,y) \cdot \tau (y,0)} $$ is finite at the critical point, where τ(x, y) is the probability that theExpand
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Self-avoiding walk in five or more dimensions I. The critical behaviour
We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford≧5. We prove that the numbercn ofn-step self-avoiding walks satisfiescn~Aμn, where μ isExpand
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Mean-Field Behaviour and the Lace Expansion
These lectures describe the lace expansion and its role in proving mean-field critical behaviour for self-avoiding walks, lattice trees and animals, and percolation, above their upper criticalExpand
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On the upper critical dimension of lattice trees and lattice animals
We give a rigorous proof of mean-field critical behavior for the susceptibility (γ=1/2) and the correlation length (v=1/4) for models of lattice trees and lattice animals in two cases: (i) for theExpand
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Mean-field critical behaviour for correlation length for percolation in high dimensions
SummaryExtending the method of [27], we prove that the corrlation length ξ of independent bond percolation models exhibits mean-field type critical behaviour (i.e. ξ(p∼(pc−p)−1/2 asp↗pc) in twoExpand
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Extremely quick thermalization in a macroscopic quantum system for a typical nonequilibrium subspace
The fact that macroscopic systems approach thermal equilibrium may seem puzzling, for example, because it may seem to conflict with the time-reversibility of the microscopic dynamics. We here proveExpand
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The number and size of branched polymers in high dimensions
We consider two models of branched polymers (lattice trees) on thed-dimensional hypercubic lattice: (i)the nearest-neighbor model in sufficiently high dimensions, and (ii) a “spread-out” orExpand
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Critical behavior in gravitational collapse of a perfect fluid
To confirm the scenario of critical behavior in gravitational collapse in a previous paper we carry out a rather complete analysis for perfect fluids with pressure proportional to density, in a wideExpand
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New Application of the Transient Grating Method to a Photochemical Reaction: The Enthalpy, Reaction Volume Change, and Partial Molar Volume Measurements
A new application of the time-resolved transient grating method for measuring the enthalpy and reaction volume changes in a photochemical reaction is described in detail. From the temporal profile ...
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Absorption of CO/sub 2/ and CO gases and furfural in insulating oil into paper insulation in oil-immersed transformers
This paper relates to diagnostic methods for oil-immersed transformers. Diagnosis of internal condition of oil-immersed transformers using dissolved gas analysis technique is widely performed toExpand
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