一般注記出版タイプ： VoR
In the context of randomly fluctuating interfaces in (1+1)-dimensions we consider the Kardar-Parisi-Zhang universality class. In the last 20 years integrable techniques were developed to study representative models in this class and mathematical predictions have been experimentally verified with extreme precision. The most general integrable model available to study KPZ phenomena is the Higher Spin Vertex Model (HSVM) and in this thesis we extend the theory of its integrability. This is accomplished through the study of two families of special symmetric functions: the spin Hall-Littlewood ($\mathsf{F}$) and the spin $q$-Whittaker ($\mathbb{F}$) functions. Yang-Baxter relations endow $\mathsf{F}$ and $\mathbb{F}$ of symmetries and in parallel offer them probabilistic meaning via bijectivization techniques. Random fields weighted by $\mathsf{F}$ and $\mathbb{F}$ possess Markov projections giving rise to the HSVM. Novel eigenrelations for these special functions allow a systematic study of one point statistics of the fields. From these we recover the $1:2:3$ scaling and characteristic fluctuations for the HSVM and its various specializations.
identifier:oai:t2r2.star.titech.ac.jp:50536757
連携機関・データベース国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
提供元機関・データベース東京科学大学 : 東京科学大学リサーチリポジトリ(T2R2)