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ABSTRACT:
We study the probability distribution P(x,t) for the head of a
directed polymer in a random medium in 1+1 dimensions. We find
that, as a function of the scaling variable u=|x|/t2/3,
the behavior of the probability distribution changes abruptly at
uc=1.2. Its universal part is given by P
~exp(-auy)
where the exponent a is distributed for
different samples according to P(a)
=N exp[-f(a)uy].
For 0.25<u<
uc, y=2.1+/-0.1 and the multifractal measure
f(a) is a convex function with a
minimum at atyp, which is
the exponent associated with a typical sample of the disorder. For
u>>uc, y=3.0+/-0.1 and f(a)
becomes trivial.
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