Long-range angular correlations of waves in a tube geometry

We show the existence of unusual angular correlations for transmitted and reflected waves for a random medium in the shape of a long tube. The brightness of the speckle spot extends much above its normal angular size =/W (where W is the width of the tube) and falls off only as a power law with oscillatory strength. We show a gradual disappearance of the memory effect as the length of the tube exceeds its width. We have also performed numerical simulations that confirm our analytical expressions for the correlation functions C1 and C2 and are able to determine the constant background correlation C3.