Random walks on the BMW monoid: an algebraic approach

作     者：Wolff, Sarah 

作者机构：Denison Univ Granville OH 43023 USA 

出 版 物：《JOURNAL OF ALGEBRAIC COMBINATORICS》 (代数组合学杂志)

年 卷 期：2019年第50卷第3期

页      面：347-361页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：NSF GRFP [DGE-1313911] 

主　　题：Metropolis algorithm Systematic scans Random walks Representation theory Semisimple algebras 

摘      要：We consider Metropolis-based systematic scan algorithms for generating Birman-Murakami-Wenzl (BMW) monoid basis elements of the BMW algebra. As the BMW monoid consists of tangle diagrams, these scanning strategies can be rephrased as random walks on links and tangles. We also consider the Brauer algebra and use Metropolis-based scans to generate Brauer diagrams, giving rise to random walks on perfect matchings. Taking an algebraic perspective, we translate these walks into left multiplication operators in the BMW algebra and so give an algebraic interpretation of the Metropolis algorithm in this setting.