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We present an exact representation for decaying ZZ-branes within the dualmatrix model formulation of c=1 string theory. It is shown how to trade theinsertion of decaying ZZ-branes for a shift of the closed string background.Our formlaism allows us to demonstrate that the conjectured world-sheetmechanism behind the open-closed dualities (summing over disc insertions) isrealized here in a clear way. On the way we need to clarify certain infraredissues - insertion of ZZ-branes creates solitonic superselection sectors.Comment: 37 pages; v2: Minor correction

On tachyon condensation and open-closed duality in thec= 1 string theory