We calculate the cumulants of the charge transmitted through a chaotic cavi
ty in the limit that the two openings have a large number of scattering cha
nnels. The shot noise, which is the second cumulant, is known to be insensi
tive to dephasing in this limit. Unexpectedly, the fourth and higher cumula
nts are found to depend on dephasing: A semiclassical theory and a quantum
mechanical model with strong dephasing give a result different from a fully
phase-coherent quantum mechanical theory. (C) 2001 Elsevier Science B.V. A
ll rights reserved.