Geodesic rays in the uniform infinite half-planar quadrangulation return to the boundary
نویسندگان
چکیده
منابع مشابه
A view from infinity of the uniform infinite planar quadrangulation
We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ). Our approach is based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context of infinite trees, in the spirit of previous work [11, 27, 30]. However, we release the positivity constraint on the labels of trees which was imposed in these references, so that our construction is technically much ...
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We introduce and study the uniform infinite planar quadrangulation (UIPQ) with a boundary via an extension of the construction of [14]. We then relate this object to its simple boundary analog using a pruning procedure. This enables us to study the aperture of these maps, that is, the maximal distance between two points on the boundary, which in turn sheds new light on the geometry of the UIPQ....
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We study the pioneer points of the simple random walk on the uniform infinite planar quadrangulation (UIPQ) using an adaptation of the peeling procedure of [3] to the quadrangulation case. Our main result is that, up to polylogarithmic factors, n3 pioneer points have been discovered before the walk exits the ball of radius n in the UIPQ. As a result we verify the KPZ relation [28] in the partic...
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15 صفحه اولInfinite geodesic rays in the space of Kähler potentials
It has been shown by Mabuchi ([18]), Semmes ([20]) and Donaldson ([11]) that the space of Kähler metrics cohomologous to a fixed one has a riemannian structure of infinite dimensional symmetric space of negative curvature. Being its dimension not finite, the usual properties about existence, uniqueness and regularity for geodesics do not hold a priori. They appear crucial in a number of applica...
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ژورنال
عنوان ژورنال: Latin American Journal of Probability and Mathematical Statistics
سال: 2016
ISSN: 1980-0436
DOI: 10.30757/alea.v13-40