Julia sets of random exponential maps

For a bounded sequence omega = (lambda(n))(n=1)(infinity) of positive real numbers we consider the exponential functions f(lambda n) (z) = lambda(n)e(z) and the compositions F-omega(n) := f(lambda n) circle f lambda(n-1) circle...circle f(lambda 1). The definitions of Julia and Fatou sets are naturally generalized to this setting. We study how the Julia set depends on the sequence omega. Among other results, we prove that for the sequence lambda(n) = 1/e + 1/n(p) with p < 1/2, the Julia set is the whole plane.