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Edge effects in the depinned phase of flux lines in hollow superconductingcylinder with columnar defects and electric current along the cylinder areinvestigated. Far from the ends of the cylinder vortices are distributed almostuniformly (delocalized). Nevertheless, near the edges these free vortices comecloser together and form well resolved dense bunches. A semiclassical pictureof this localization after depinning is described. For a large number ofvortices their density $\rho(x)$ has square root singularity at the border ofthe bunch ($\rho(x)$ is semicircle in the simplest case). However, by tuningthe strength of current, the various singular regimes for $\rho(x)$ may bereached. Remarkably, this singular behaviour reproduces the phase transitionsdiscussed during the past decade within the random matrix regularization of2d-Gravity.Comment: 4 pages, REVTEX, 2 eps figure

Vortices in a Superconducting Cylinder: Edge Effects in the Depinned Phase