180 citations · 357 across the 58 of their papers we have counts for
6 papers · 1 filter
Sharp probability estimates for random walks with barriers
Kevin Ford
We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hol…
Sharp probability estimates for generalized Smirnov statistics
Kevin Ford
We give sharp, uniform estimates for the probability that the empirical distribution function for n uniform-[0,1] random variables stays to one side of a given line.
Localized large sums of random variables
Kevin Ford, Gerald Tenenbaum
We study large partial sums, localized with respect to the sums of variances, of a sequence of centered random variables. An application is given to the distribution of prime facto…
On curves over finite fields with Jacobians of small exponent
Kevin Ford, Igor Shparlinski
We show that finite fields over which there is a curve of a given genus g with its Jacobian having a small exponent, are very rare. This extends a recent result of W. Duke in the c…
Integers with a divisor in (y,2y]
Kevin Ford
We give a relatively short proof of one of the central cases of the main theorem from the paper "The distribution of integers with a divisor in a given interval", math.NT/0401223.…
The distribution of integers with at least two divisors in a short interval
Kevin Ford, Gerald Tenenbaum
Let H(x,y,z) be the number of integers with a divisor in (y,z] and let H_1(x,y,z) be the number of integers with exactly one such divisor. When y and z are close, i…