Proof of the Path Localization Conjecture for Directed Polymers
نویسندگان
چکیده
منابع مشابه
The directed path partition conjecture
The Directed Path Partition Conjecture is the following: If D is a digraph that contains no path with more than λ vertices then, for every pair (a, b) of positive integers with λ = a + b, there exists a vertex partition (A, B) of D such that no path in D〈A〉 has more than a vertices and no path in D〈B〉 has more than b vertices.We develop methods for finding the desired partitions for various cla...
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Let D be a digraph. A path partition of D is called k-optimal if the sum of the k-norms of its paths isminimal. The k-norm of a path P ismin(|V (P)|, k). Berge’s path partition conjecture claims that for every k-optimal path partition P there are k disjoint stable sets orthogonal to P . For general digraphs the conjecture has been proven for k = 1, 2, λ − 1, λ, where λ is the length of a longes...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2019
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-019-03533-1