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If we introduce stochasticity in the evolution rules, the mean square displacement of the walker, $<R_{N}^{2}> \\sim N^{2\\nu}$, shows a crossover from the Euler"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0906.5506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-06-30T12:57:15Z","cross_cats_sorted":[],"title_canon_sha256":"c70705e02a62ec2ecc65564c950d9cc18cfa7f4a061db7bef9813b561c37e2b1","abstract_canon_sha256":"343a42846dbd333c0bfa6ee52755a8ddf5af85fcb011faa99e8a15237d64af1c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:42.815366Z","signature_b64":"LWNxdW5OpPp9spmUzZBFd5S1YA1H1JuRQTeLdSiVoju2vQ4wHRTWjriNbdEWgD/H56GUM0C2M/MeD1BBOKT9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a477b2eda6498bbaceb4122d5dd5201fa78440ccff48c3909105a82c786808a9","last_reissued_at":"2026-05-18T03:43:42.814710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:42.814710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic shape of the region visited by an Eulerian Walker","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Deepak Dhar, Rajeev Kapri","submitted_at":"2009-06-30T12:57:15Z","abstract_excerpt":"We study an Eulerian walker on a square lattice, starting from an initially randomly oriented background using Monte Carlo simulations. 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