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All our analytical findings are supported with numerical simulations.We revisit the problem of an elastic line (such as a vortex line in a superconductor) subject to both columnar disorder and point disorder in dimension d=1+1. Upon applying a transverse field, a delocalization transition is expected, beyond which the line is tilted macroscopically. We investigate this transition in the fixed tilt angle ensemble and within a "one-way" model where backward jumps are neglected. From recent results about directed polymers in the mathemati
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