Upper tails for triangles
نویسندگان
چکیده
منابع مشابه
Assignment, Hierarchies and Upper Tails
This paper examines whether changes in upper tails could explain increases in inequality in recent decades. First, methods are discussed that would determine the relative contributions of educational di¤erentials or variance of outcomes within educational levels to overall inequality. Preliminary analysis suggests that educational di¤erentials could not explain increases in inequality. The pape...
متن کاملUpper Tails for Subgraph Counts in Random Graphs
Let G be a fixed graph and let XG be the number of copies of G contained in the random graph G(n, p). We prove exponential bounds on the upper tail of XG which are best possible up to a logarithmic factor in the exponent. Our argument relies on an extension of Alon’s result about the maximum number of copies of G in a graph with a given number of edges. Similar bounds are proved for the random ...
متن کاملSub-Gaussian Tails for the Number of Triangles in G( n, p)
Let X be the random variable that counts the number of triangles in the random graph G(n, p). We show that for some absolute constant c, the probability that X deviates from its expectation by at least λVar(X) is at most e 2 , provided that n(lnn) ≤ p ≤ n(lnn), λ = ω(lnn) and λ ≤ min{(np)1/2, np, n1/6}.
متن کاملUpper Tails and Independence Polynomials in Random Graphs
The upper tail problem in the Erdős–Rényi random graph G ∼ Gn,p asks to estimate the probability that the number of copies of a graph H in G exceeds its expectation by a factor 1 + δ. Chatterjee and Dembo showed that in the sparse regime of p→ 0 as n→∞ with p ≥ n−α for an explicit α = αH > 0, this problem reduces to a natural variational problem on weighted graphs, which was thereafter asymptot...
متن کاملAutomated Proofs in Geometry : Computing Upper Bounds for the Heilbronn Problem for Triangles
The Heilbronn problem for triangle[Wei] is defined as follows: place N points inside a triangle of unit area, so as to maximize the area of the smallest triangle obtained by choosing 3 points among N. Several authors worked towards finding lower bounds or optimal configurations of points. In this paper, we propose upper bounds for those problems, obtained by a method of automated theorem proving.
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: Random Structures & Algorithms
سال: 2011
ISSN: 1042-9832
DOI: 10.1002/rsa.20382