Asymptotic shape of the convex hull of isotropic log-concave random vectors
نویسندگان
چکیده
منابع مشابه
Convex Hull Asymptotic Shape Evolution
The asymptotic properties of Rapidly exploring Random Tree (RRT) growth in large spaces is studied both in simulation and analysis. The main phenomenon is that the convex hull of the RRT reliably evolves into an equilateral triangle when grown in a symmetric planar region (a disk). To characterize this and related phenomena from flocking and swarming, a family of dynamical systems based on incr...
متن کاملA reverse entropy power inequality for log-concave random vectors
We prove that the exponent of the entropy of one dimensional projections of a log-concave random vector defines a 1/5-seminorm. We make two conjectures concerning reverse entropy power inequalities in the log-concave setting and discuss some examples. 2010 Mathematics Subject Classification. Primary 94A17; Secondary 52A40, 60E15.
متن کاملAlpha-Concave Hull, a Generalization of Convex Hull
Bounding hull, such as convex hull, concave hull, alpha shapes etc. has vast applications in different areas especially in computational geometry. Alpha shape and concave hull are generalizations of convex hull. Unlike the convex hull, they construct non-convex enclosure on a set of points. In this paper, we introduce another generalization of convex hull, named alpha-concave hull, and compare ...
متن کاملA Lower Bound on the Differential Entropy of Log-Concave Random Vectors with Applications
We derive a lower bound on the differential entropy of a log-concave random variable X in terms of the p-th absolute moment of X. The new bound leads to a reverse entropy power inequality with an explicit constant, and to new bounds on the rate-distortion function and the channel capacity. Specifically, we study the rate-distortion function for log-concave sources and distortion measure |x− x̂|,...
متن کاملConvex hull for intersections of random lines
Numerous problems can be reduced to finding the convex hull of a set of points – halfspace intersection, Delaunay triangulation, etc. An algorithm for finding the convex hull in the plane, known as Graham scan [5], achieves an O(n log n) running time. This algorithm is optimal in the worst case. Another algorithm [6] for the same problem runs in O(nh) time, where h is the number of hull points,...
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: Advances in Applied Mathematics
سال: 2016
ISSN: 0196-8858
DOI: 10.1016/j.aam.2016.01.004