  It is shown that statistics of records for time series generated by random
walks are independent of the details of the jump distribution, as long as the
latter is continuous and symmetric. In N steps, the mean of the record
distribution grows as the sqrt(4N/pi) while the standard deviation grows as
sqrt((2-4/pi) N), so the distribution is non-self-averaging. The mean shortest
and longest duration records grow as sqrt(N/pi) and 0.626508... N,
respectively. The case of a discrete random walker is also studied, and similar
asymptotic behavior is found.
