Consider a simple random walk on ℤ with coloring of ℤ. Look at the sequence first N steps taken in walk, together colors visited locations. We call this record. From record one can deduce interval that was visited, which is size approximately $$\sqrt $$ . This called scenery reconstruction. Now suppose an adversary may change δN entries obtained. What we from about now? In paper show it likely ...

This thesis aim is to present results on a stochastic model called reinforced random walk. This process was conceived in the late 1980’s by Coppersmith and Diaconis and can be regarded as a generalization of a random walk on a weighted graph. These reinforced walks have non-homogeneous transition probabilities, which arise from an interaction between the process and the weights. We survey artic...

This note presents a proof of Pólya’s random walk theorem using classical methods from special function theory and asymptotic analysis.