Marco Aymone

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math.PR2020

Bernoulli Hyperplane Percolation

Marco Aymone, Marcelo R. Hilário, Bernardo N. B. de Lima +1

We study a dependent site percolation model on the $n$ -dimensional Euclidean lattice where, instead of single sites, entire hyperplanes are removed independently at random. We exte…

math.PR2020

Law of the iterated logarithm for a random Dirichlet series

Marco Aymone, Susana Frómeta, Ricardo Misturini

Let $(X_{n})_{n \in N}$ be a sequence of i.i.d. random variables with distribution $P (X_{1} = 1) = P (X_{1} = - 1) = 1/2$ . Let $F (σ) = \sum_{n = 1}^{\infty} X_{n} n^{- σ}$ . We prove…

math.PR2019

Real zeros of random Dirichlet series

Marco Aymone

Let $F (σ)$ be the random Dirichlet series $F (σ) = \sum_{p \in P} \frac{X _{p}}{p ^{σ}}$ , where $P$ is an increasing sequence of positive real numbers and $(X_p)_{p\in\mat…