## Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

## If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

# The Almost Sure Number of Pairwise Sums for Certain Random Integer Subsets Considered by P. Erdös

Michael J. Klass
Lecture Notes-Monograph Series
Vol. 35, Game Theory, Optimal Stopping, Probability and Statistics (2000), pp. 179-189
Stable URL: http://www.jstor.org/stable/4356089
Page Count: 11
Preview not available

## Abstract

Fix any λ > 0 and let X1, X2,... be independent and identically distributed 0-1 valued random variables such that $P(X_{j}=1)=\text{min}\left\{\sqrt{\frac{2\lambda}{\pi}\frac{\text{ln}\ j}{j}},1\right\}$. Let $G_{n}=\sum_{j=1}^{\lfloor n/2\rfloor }X_{j}X_{n-j}$. Gn is the number of times two numbers from the random set $S\equiv \{j\colon X_{j}=1\}$ add to n. We evaluate the almost sure limits $\underset n\rightarrow \infty \to{\text{lim inf}}\frac{G_{n}}{EG_{n}}\equiv c_{1}(\lambda)$ and $c_{2}(\lambda)\equiv \underset n\rightarrow \infty \to{\text{lim sup}}\frac{G_{n}}{EG_{n}}$, showing that \$0\leq c_{1}(\lambda)<1

• 179
• 180
• 181
• 182
• 183
• 184
• 185
• 186
• 187
• 188
• 189
s