Zygouras, Nikolaos Semidirected random polymers: strong disorder and localization. (English) Zbl 1477.60143 Actes Rencontres C.I.R.M. 2, No. 1, 47-48 (2010). Summary: Semi-directed, random polymers can be modeled by a simple random walk on \(\mathbb Z^d\) in a random potential \(-(\lambda + \beta \omega(x))_{x \in \mathbb Z^{d}}\), where \(\lambda > 0\), \(\beta > 0\) and \((\omega(x))_{x \in \mathbb Z^{d}}\) is a collection of i.i.d., nonnegative random variables. We identify situations where the annealed and quenched costs, that the polymer pays to perform long crossings are different. In these situations we show that the polymer exhibits localization. MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82D60 Statistical mechanics of polymers Keywords:semidirected random polymers × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Giacomin, Giacomin; Lacoin, Hubert; Toninelli, Fabio L.; \(Marginal relevance of disorder for pinning models.\) Comm. Pure Appl. Math. 63 (2010) 233-265. · Zbl 1189.60173 [2] Lacoin, Hubert; \(New bounds for the free energy of directed polymer in dimension 1+1 and 1+2.\) Comm. Math. Phys. 294 (2010) 471-503. · Zbl 1227.82098 [3] Ioffe, Dmitry; Velenik, Yvan; \(Crossing random walks and stretched polymers at weak disorder.\) arXiv:1002.4289 · Zbl 1251.60074 [4] Vargas, Vincent; \(Strong localization and macroscopic atoms for directed polymers\) Prob. Theory Rel. Fields Volume 138, Numbers 3-4 (2007) · Zbl 1113.60097 [5] Zygouras, N.; \(Strong disorder in semidirected random polymers. \) arxiv.org/abs/1009.2693 Copyright Cellule MathDoc 2018 · Zbl 1290.82013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.