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We use the tangent method to investigate the arctic curve in a model ofnon-intersecting lattice paths with arbitrary fixed starting points alignedalong some boundary and whose distribution is characterized by some arbitrarypiecewise differentiable function. We find that the arctic curve has a simpleexplicit parametric representation depending of this function, providing uswith a simple transform that maps the arbitrary boundary condition to thearctic curve location. We discuss generic starting point distributions as wellas particular freezing ones which create additional frozen domains adjacent tothe boundary, hence new portions for the arctic curve. A number of examples arepresented, corresponding to both generic and freezing distributions.

Arctic curves for paths with arbitrary starting points: a tangent method approach