2011/08/25 by Daniel J. Fresen, Fresen, Daniel
Computer Science · Economics, Econometrics and Finance · Environmental Science · #26B35 #60F05 #60G55 #60G70 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Functional Analysis (math.FA) #Probability (math.PR) #Soil Geostatistics and Mapping #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1108.5011
openalex publication_date 2011/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We observe that approximate copies of the function Λn:ℝn→ (0,∞ ) defined by Λn(x)=exp ( -x1-π∑i=2nxi2) appear in the tails of a large class of functions, with properties related to coordinate independence, convexity, homotheticity, and homogeneity. The function Λn is an entropy maximizer (on a half-space) that is uniquely determined by a homogeneity condition together with rotational invariance about the x1 direction and its behavior near the origin. These results are connected to the limiting Poisson point processes found near the edges of large random samples, as well as the conditioning of random vectors on certain rare events, and can be thought of as variations of Laplace's method for estimating integrals.