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تسجيل مستخدم جديدDirected polymers on infinite graphs
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We study the directed polymer model for general graphs (beyond $mathbb Z^d$) and random walks. We provide sufficient conditions for the existence or non-existence of a weak disorder phase, of an $L^2$ region, and of very strong disorder, in terms of properties of the graph and of the random walk. We study in some detail (biased) random walk on various trees including the Galton Watson trees, and provide a range of other examples that illustrate counter-examples to intuitive extensions of the $mathbb Z^d$/SRW result.
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I discuss models for a continuum directed random polymer in a disordered environment in which the polymer lives on a fractal called the textit{diamond hierarchical lattice}, a self-similar metric space forming a network of interweaving pathways. This
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We prove a distributional limit theorem conjectured in [Journal of Statistical Physics 174, No. 6, 1372-1403 (2019)] for partition functions defining models of directed polymers on diamond hierarchical graphs with disorder variables placed at the gra
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