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A growing self-avoiding walk (GSAW) is a stochastic process that starts fromthe origin on a lattice and grows by occupying an unoccupied adjacent latticesite at random. A sufficiently long GSAW will reach a state in which alladjacent sites are already occupied by the walk and become trapped, terminatingthe process. It is known empirically from simulations that on a square lattice,this occurs after a mean of 71 steps. In Part I of a two-part series ofmanuscripts, we consider simplified lattice geometries only two sites high("ladders") and derive generating functions for the probability distribution ofGSAW trapping. We prove that a self-trapping walk on a square ladder willbecome trapped after a mean of 17 steps, while on a triangular ladder trappingwill occur after a mean of 941/48 (~19.6 steps). We discuss additionalimplications of our results for understanding trapping in the "infinite" GSAW.

Exactly-Solvable Self-Trapping Lattice Walks. Part I: Trapping in Ladder Graphs