{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:27Z","timestamp":1753893867328,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We give a combinatorial proof that a random walk attains a unique maximum with probability at least $1\/2$. For closed random walks with uniform step size, we recover Dwass's count of the number of length $\\ell$ walks attaining the maximum exactly $k$ times. We also show that the probability that there is both a unique maximum and a unique minimum is asymptotically equal to $\\frac14$ and that the probability that a Dyck word has a unique minimum is asymptotically $\\frac12$.<\/jats:p>","DOI":"10.37236\/5330","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:07:52Z","timestamp":1578694072000},"source":"Crossref","is-referenced-by-count":0,"title":["A Note on Maxima in Random Walks"],"prefix":"10.37236","volume":"23","author":[{"given":"Joseph","family":"Helfer","sequence":"first","affiliation":[]},{"given":"Daniel T.","family":"Wise","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2016,1,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p17\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v23i1p17\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:36:55Z","timestamp":1579239415000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v23i1p17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,1,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,1,11]]}},"URL":"https:\/\/doi.org\/10.37236\/5330","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2016,1,22]]},"article-number":"P1.17"}}