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Keywords: Random matrix, eigenvalues, asymptotic independence, Gaussian unitary
In this paper, we will compute precise asymptotics for the return probability on the lamplighter group as well as bounds for the distribution of the position of a random walk away
The special case of exponentially distributed random variables was studied by Engel and Leuenberger (2003): Such random variables satisfy the first digit law only ap- proximatively,
In Section 2 we first review the decomposition of the size-biased Galton-Watson tree along the distin- guished line of descent of a particle chosen purely at random and give a
We will see in Section 4.1 that, assuming the Lifshitz tail effect in [ 12 ] , our result indeed derives the correct upper bound of the quenched asymptotics for the Brownian
Among several examples, such as random variables which depend on infinitely many Rademacher variables, we provide three main applications: (i) to CLTs for multilinear forms belonging
To prove this theorem we extend the bounds proved in [ 2 ] for the continuous time simple random walk on (Γ , µ ) to the slightly more general random walks X and Y defined
(Ordinary differential equations constitute a special case; we will mention those later.) We define the partial derivatives of the dependent variables as new variables (prolongation)
