论文标题
离散的惠特克过程
Discrete Whittaker processes
论文作者
论文摘要
我们考虑在给定形状（并满足某些约束）的非阴性整数阵列上的马尔可夫链，该数组与基本$ sl密切相关（r+1，\ mathbb {r}）$ whittaker函数和toda lattice。在索引零情况下，阵列是反向平面分区。我们表明，这座马尔可夫连锁店具有非平凡的马尔可夫预测和独特的入口法，从阵列开始，所有条目等于$+\ infty $。我们还讨论了与布朗运动的假想指数功能的连接，布朗运动是一种纯粹想象中的疾病，相互作用的角生长过程和离散$δ$ bose气体，对其他根系的扩展以及对某些低等级示例的命中概率。
We consider a Markov chain on non-negative integer arrays of a given shape (and satisfying certain constraints) which is closely related to fundamental $SL(r+1,\mathbb{R})$ Whittaker functions and the Toda lattice. In the index zero case the arrays are reverse plane partitions. We show that this Markov chain has non-trivial Markovian projections and a unique entrance law starting from the array with all entries equal to $+\infty$. We also discuss connections with imaginary exponential functionals of Brownian motion, a semi-discrete polymer model with purely imaginary disorder, interacting corner growth processes and discrete $δ$-Bose gas, extensions to other root systems, and hitting probabilities for some low rank examples.
