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Limit theorems for Random Walk excursion conditioned to have a typical area. (arXiv:1709.06448v2 [math.PR] UPDATED)
来源于:arXiv
We derive a functional central limit theorem for the excursion of a random
walk conditioned on sweeping a prescribed geometric area. We assume that the
increments of the random walk are integer-valued, centered, with a third moment
equal to zero and a finite fourth moment. This result complements the work of
\citep{DKW13} where local central limit theorems are provided for the geometric
area of the excursion of a symmetric random walk with finite second moments.
Our result turns out to be a key tool to derive the scaling limit of the
\emph{Interacting Partially-Directed Self-Avoiding Walk} at criticality which
is the object of a companion paper \citep{CarPet17a}. This requires to derive a
reinforced version of our result in the case of a random walk with Laplace
symmetric increments. 查看全文>>