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Alternatively, we can prove a result along the lines of Theorem 3.1 using results on integral points of bounded degree on curves.. Here φ is Euler’s
We start by reviewing facts about Brownian motion in a rectangle with the intent of using conformal invariance to relate these results to regions that are conformally equivalent to
We study an infinite white α -stable systems with unbounded interactions, and prove the exis- tence of a solution by Galerkin approximation and an exponential mixing property by an
The behaviour of the horizontal projection of the random walk is less obvious: in Sections 3, 4 and 5 we prove that the expected values of the horizontal distance, of its
Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and
We prove an invariance principle for the quenched mean of the position of the walk on crossing level n ; there is a nice martingale structure in the background as will be evident in
Then, to prove IDLA inner bound, we need to show that for each vertex v ∈ V the Green function from 0 and expected exit time from a ball around 0 of a random walk starting at v ,
In this paper we prove a strong approximation result for a mixing sequence of identically distributed random variables with infinite variance, whose distribution is symmetric and
