Capacity of the range in dimension 5

Faisant l’hypoth` ese fr´ equentiste que les donn´ ees sont une r´ ealisation du mod` ele statis- tique pour une valeur θ ∗ du param` etre (inconnue), cette approche recherche

Then, we want to use this speed of convergence to prove the central limit theorem and the law of the iterated logarithm for starting points having good diophantine properties.. In

We also study the range of random walks in random scenery, from which the asymptotic behaviour of the range of the first coordinate of the Campanino and P´etritis random walk can

In the first section we define the rule to be analyzed and give analytical results about the limit of capacity of the perceptron for this rule and the minimum error

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We obtain estimates for large and moderate deviations for the capacity of the range of a random walk on Z d , in dimension d ≥ 5, both in the upward and downward directions..

They suggest that conditioned on having a small boundary of the range, in dimension three a (large) fraction of the walk is localized in a ball of volume n/ε, whereas in dimension

In the eighties, Lawler established estimates on intersection probabilities for random walks, which are relevant tools for estimating the expected capacity of the range (see