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Each of the studied decompositions is associated to a class of commutative rings for which all systems can be decomposed accordingly.. Finally, examples are shown of
The results of this section are valid in any dimension d. They describe some essential facts concerning the geometry of the cycles of the energy landscape of the Ising model.
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
Molloy, Very rapidly mixing Markov chains for 2∆-colourings and for independent sets in a 4-regular graph, Random Struc. Tetali, Mathematical aspects of mixing times in Markov
In the case of a Markov chain over an infinite state space with a unique stationary distribution, the notion of a mixing time depends on the state of origination of the
We emphasise that the scaling limit of the kinetic prudent walk seems to be different from the scaling limit of the uniform prudent walk studied in Combinatorics... The inset is
Using Talagrand’s abstract concentration inequality in product spaces and the related kernel method for empirical processes [14] we will first prove a general result that
In this note the almost sure convergence of stationary, ϕ -mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is
