  In the weak backscattering limit, point contact tunneling between quantum
Hall edges is well described by a Poissonian process where Laughlin
quasiparticles tunnel independently, leading to the unambiguous measurement of
their fractional charges. In the strong backscattering limit, the tunneling is
well described by a Poissonian process again, but this time involving real
electrons. In between, interactions create essential correlations, which we
untangle exactly in this Letter. Our main result is an exact closed form
expression for the probability distribution of the charge $N(t)$ that tunnels
in the time interval $t$. Formally, this distribution corresponds to a sum of
independent Poisson processes carrying charge $\nu e$, $2\nu e$, etc., or,
after resummation, processes carrying charge $e$, $2e$, etc. In the course of
the proof, we compare the integrable and Keldysh approaches, and find, as a
result of spectacular cancellations between perturbative integrals, the
expected agreement.
