{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,10]],"date-time":"2026-10-10T07:34:29Z","timestamp":1791617669351,"version":"4.3.4"},"reference-count":21,"publisher":"Cambridge University Press (CUP)","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p>Simple random walks on a partially directed version of<jats:bold>Z<\/jats:bold><jats:sup>2<\/jats:sup>are considered. More precisely, vertical edges between neighbouring vertices of<jats:bold>Z<\/jats:bold><jats:sup>2<\/jats:sup>can be traversed in both directions (they are undirected) while horizontal edges are one-way. The horizontal orientation is prescribed by a random perturbation of a periodic function; the perturbation probability decays according to a power law in the absolute value of the ordinate. We study the type of simple random walk that is recurrent or transient, and show that there exists a critical value of the decay power, above which it is almost surely recurrent and below which it is almost surely transient.<\/jats:p>","DOI":"10.1017\/s0021900200011980","type":"journal-article","created":{"date-parts":[[2016,3,29]],"date-time":"2016-03-29T10:51:14Z","timestamp":1459248674000},"page":"1065-1080","source":"Crossref","is-referenced-by-count":3,"title":["Type Transition of Simple Random Walks on Randomly Directed Regular Lattices"],"prefix":"10.1017","volume":"51","author":[{"given":"Massimo","family":"Campanino","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dimitri","family":"Petritis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2016,2,4]]},"reference":[{"key":"S0021900200011980_ref18","volume-title":"Theoretical Probability for Applications","year":"1994"},{"key":"S0021900200011980_ref19","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.56.4967"},{"key":"S0021900200011980_ref16","doi-asserted-by":"publisher","DOI":"10.1051\/ps:2008019"},{"key":"S0021900200011980_ref15","doi-asserted-by":"publisher","DOI":"10.1029\/WR016i005p00901"},{"key":"S0021900200011980_ref9","volume-title":"Random Walks and Electric Networks","year":"1984"},{"key":"S0021900200011980_ref8","volume":"18","year":"2013","journal-title":"Electron. 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