We consider a one-dimensional transient cookie random walk. It is known from
a previous paper that a cookie random walk (Xn) has positive or zero speed
according to some positive parameter α>1 or ≤1. In this article,
we give the exact rate of growth of (Xn) in the zero speed regime, namely:
for 0<α<1, Xn/n2α+1 converges in law to a
Mittag-Leffler distribution whereas for α=1, Xn(logn)/n converges
in probability to some positive constant