The Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.research

Topic: Quasi-random numbers (almost)
Replies: 0  

Advanced Search

Back to Topic List Back to Topic List  
Arthur Rubin

Posts: 1
Registered: 10/11/17
Quasi-random numbers (almost)
Posted: Oct 11, 2017 9:06 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


With a irrational, let x(n) = {a n}, the fractional part of {a n}.

What can be said about
(1) The "distribution" of sum (k = 1 to n) x(k).  Any bounds (upper or
lower) for the deviation of the sample CDF of x(k) from uniform, or the
maximum or minimum gap.
(2) With X(k) = {U + x(k)}, for a single U, uniform on (0, 1).
What can be said about the distribution of S(n) = sum(k=1 to n)X(k).
 E(S(n)) = n/2, and I can calculate Var(S(n)) as an algebraic function
of x(k), but I have not calculated asymptotic bounds.

--  
Arthur L. Rubin



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2017. All Rights Reserved.