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

We use a tangent method approach to obtain the arctic curve in a model of non-intersecting lattice
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.

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