 
Summary: Acta Math. Hungar., 121 (3) (2008), 243275.
DOI: 10.1007/s1047400871177
First published online September 19, 2008
DISTRIBUTION OF THE MAXIMA
OF RANDOM TAKAGI FUNCTIONS
P. C. ALLAART
Mathematics Department, University of North Texas, P.O. Box 311430, Denton, TX 762031430
email: allaart@unt.edu
(Received June 12, 2007; revised April 21, 2008; accepted May 4, 2008)
Abstract. This paper concerns the maximum value and the set of maximum
points of a random version of Takagi's continuous, nowhere dierentiable function.
Let F(x) :=
n=1
1
2
n1
n(2n1
x), x R, where 1, 2, . . . are independent,
identically distributed random variables taking values in {1, 1}, and is the
tent map dened by (x) = 2 dist (x, Z). Let p := P (1 = 1), M := max F(x) :
