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| ファイル | 記述 | サイズ | フォーマット | |
|---|---|---|---|---|
| s00220-019-03585-3.pdf | 321.77 kB | Adobe PDF | 見る/開く |
| タイトル: | Biased Random Walk on the Trace of Biased Random Walk on the Trace of … |
| 著者: | Croydon, David   Holmes, Mark |
| 発行日: | Apr-2020 |
| 出版者: | Springer Nature |
| 誌名: | Communications in Mathematical Physics |
| 巻: | 375 |
| 号: | 2 |
| 開始ページ: | 1341 |
| 終了ページ: | 1372 |
| 抄録: | We study the behaviour of a sequence of biased random walks (X(i))i≥0 on a sequence of random graphs, where the initial graph is Zd and otherwise the graph for the ith walk is the trace of the (i−1)st walk. The sequence of bias vectors is chosen so that each walk is transient. We prove the aforementioned transience and a law of large numbers, and provide criteria for ballisticity and sub-ballisticity. We give examples of sequences of biases for which each (X(i))i≥1 is (transient but) not ballistic, and the limiting graph is an infinite simple (self-avoiding) path. We also give examples for which each (X(i))i≥1 is ballistic, but the limiting graph is not a simple path. |
| 著作権等: | This is a post-peer-review, pre-copyedit version of an article published in Communications in Mathematical Physics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00220-019-03585-3. The full-text file will be made open to the public on 3 October 2020 in accordance with publisher's 'Terms and Conditions for Self-Archiving'. This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。 |
| URI: | http://hdl.handle.net/2433/253724 |
| DOI(出版社版): | 10.1007/s00220-019-03585-3 |
| 出現コレクション: | 学術雑誌掲載論文等 |
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