منابع مشابه
Windings of Planar Random Walks and Averaged Dehn Function
We prove sharp estimates on the expected number of windings of a simple random walk on the square or triangular lattice. This gives new lower bounds on the averaged Dehn function, which measures the expected area needed to fill a random curve with a disc.
متن کاملNumerical studies of planar closed random walks
Lattice numerical simulations for planar closed random walks and their winding sectors are presented. The frontiers of the random walks and of their winding sectors have a Hausdorff dimension dH = 4/3. However, when properly defined by taking into account the inner 0-winding sectors, the frontiers of the random walks have a Hausdorff dimension dH ≈ 1.77.
متن کاملWindings of planar stable processes
Using a generalization of the skew-product representation of planar Brownian motion and the analogue of Spitzer’s celebrated asymptotic Theorem for stable processes due to Bertoin and Werner, for which we provide a new easy proof, we obtain some limit Theorems for the exit time from a cone of stable processes of index α ∈ (0, 2). We also study the case t → 0 and we prove some Laws of the Iterat...
متن کاملAnnihilating random walks and perfect matchings of planar graphs
Annihilating random walks (ARW) have been studied in the early 70’s within the theory of interacting particles systems (see [1],[2],[3] and [9]). The idea was to study a system of particles moving on a graph according to certain laws of attraction. The system we study in this paper is defined as follows: the initial system consists of particles at every site of 2 . Then, each particle simultane...
متن کاملModerate deviations for the range of planar random walks
Given a symmetric random walk in Z2 with finite second moments, let Rn be the range of the random walk up to time n. We study moderate deviations for Rn −ERn and ERn−Rn. We also derive the corresponding laws of the iterated logarithm.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1987
ISSN: 0304-4149
DOI: 10.1016/0304-4149(87)90159-1