# A tangent method derivation of the arctic curve for q -weighted paths with arbitrary starting points

paths within the first quadrant, including a q -dependent weight associated with the area delimited

by the paths. Our model is characterized by an arbitrary sequence of starting points along the

positive horizontal axis, whose distribution involves an arbitrary piecewise differentiable

function. We give an explicit expression for the arctic curve in terms of this arbitrary function

and of the parameter q . A particular emphasis is put on the deformation of the arctic curve upon

varying q , and on its limiting shapes when q tends to 0 or infinity. Our analytic results are

illustrated by a number of detailed examples.