期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021; 18 (2)
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the inters......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021; 18 (2)
In this paper we prove that the stationary harmonic measure of an infinite set in the upper planar lattice can be represented as the proper scaling li......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021; 18 (2)
We prove a law of large numbers for the order and size of the largest strongly connected component in the directed configuration model. Our result ext......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021; 18 (1)
In this paper, we prove a phase transition in the connectivity of finitary random interlacements FIu,T in Z(d), with respect to the average stopping t......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2021; 18 (1)
We consider a family of Bessel Processes that depend on the starting point x and dimension delta, but are driven by the same Brownian motion. Our main......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (1)
We study a particle system with the following diffusion branching-selection mechanism. Particles perform independent one dimensional Brownian motions ......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (1)
The key to our investigation is an improved (and in a sense sharp) understanding of the survival time of the contact process on star graphs. Using the......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (1)
We study the spatial Gibbs random graphs introduced in Mourrat and Valesin (2018) from the point of view of local convergence. These are random graphs......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (2)
We are interested in the survival probability of a population modeled by a critical branching process in an i.i.d. random environment and in the growt......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (2)
In this paper we are concerned with the two-stage contact process introduced by Krone (1999) on a high-dimensional lattice. By comparing this process ......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (2)
Consider the Ising model on ([1, 2N] x [1, 2M])boolean AND Z(2) at critical temperature with periodic boundary condition in the horizontal direction a......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2020; 17 (2)
We investigate the anisotropic stable JCIR process which is a multidimensional extension of the stable JCIR process but also a multi-dimensional analo......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2019; 16 (1)
We provide a process on the space of collections of coalescing cadlag stable paths and show convergence in an appropriate topology for coalescing stab......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2019; 16 (1)
We prove a Berry-Esseen type inequality for approximating expectations of sufficiently smooth functions f, like f = vertical bar . vertical bar(3), wi......
期刊： ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2019; 16 (1)
We consider connectivity properties of the Branching Interlacements model in Z(d), d >= 5, recently introduced by Angel, Rath and Zhu (Angel et al.......
