Gómez Donoso, Miguel2024-05-202024-05-202021-07-13https://hdl.handle.net/20.500.14468/14746The kth-passage percolation model is proposed as a generalization of the first-passage percolation model. Specific samples of k shortest simple paths in random square lattices are analyzed, revealing a potentially ultrametric structure in the overlaps between paths. The average scaling behaviour of the arrival time and its fluctuations is calculated, providing evidence that the usual Kardar–Parisi– Zhang universality class for interface growth is attained after a pre-asymptotic regime whose extent increases with k.eninfo:eu-repo/semantics/openAccesstesis de maestríapercolation problemsfluctuation phenomenainterfaces in random media