Explicit laws of large numbers for random nearest-neighbour-type graphs
نویسندگان
چکیده
منابع مشابه
Explicit laws of large numbers for random nearest-neighbour type graphs
We give laws of large numbers (in the Lp sense) for the total length of the k-nearest neighbours (directed) graph and the j-th nearest neighbour (directed) graph in Rd, d ∈ N, with power-weighted edges. We deduce a law of large numbers for the standard nearest neighbour (undirected) graph. We give the limiting constants, in the case of uniform random points in (0, 1)d, explicitly. Also, we give...
متن کاملLaws of Large Numbers for Random Linear
The computational solution of large scale linear programming problems contains various difficulties. One of the difficulties is to ensure numerical stability. There is another difficulty of a different nature, namely the original data, contains errors as well. In this paper, we show that the effect of the random errors in the original data has a diminishing tendency for the optimal value as the...
متن کاملON THE LAWS OF LARGE NUMBERS FOR DEPENDENT RANDOM VARIABLES
In this paper, we extend and generalize some recent results on the strong laws of large numbers (SLLN) for pairwise independent random variables [3]. No assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). Also Chandra’s result on Cesàro uniformly integrable r.v.’s is extended.
متن کاملCONNECTIVITY OF RANDOM k-NEAREST-NEIGHBOUR GRAPHS
LetP be a Poisson process of intensity one in a squareSn of arean. We construct a random geometric graph Gn,k by joining each point of P to its k ≡ k(n) nearest neighbours. Recently, Xue and Kumar proved that if k ≤ 0.074 log n then the probability that Gn,k is connected tends to 0 as n → ∞ while, if k ≥ 5.1774 log n, then the probability that Gn,k is connected tends to 1 as n → ∞. They conject...
متن کاملon the laws of large numbers for dependent random variables
in this paper, we extend and generalize some recent results on the strong laws of large numbers (slln) for pairwise independent random variables [3]. no assumption is made concerning the existence of independence among the random variables (henceforth r.v.’s). also chandra’s result on cesàro uniformly integrable r.v.’s is extended.
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 Probability
سال: 2007
ISSN: 0001-8678,1475-6064
DOI: 10.1017/s0001867800001786