AI 中文总结
研究 wreath 积上的群值彩色交换过程，通过表示论刻画其谱隙，在阿贝尔基群下关联离散薛定谔算子，并分类确定谱隙的极小不可约表示族。
AI 中文摘要
我们引入群值彩色交换过程，这是一类生成于换位和任意对称基群转移的 wreath 积上的连续时间随机游走。我们通过分解相关的拟正则表示并精确确定所需的不可约表示，给出了其谱隙的完整表示论刻画。对于阿贝尔基群，我们在多片上实现这些表示，并将其拉普拉斯算子与离散薛定谔算子对应。随后，我们对每类转移率选择下决定谱隙的不可约表示的极小族进行分类。
英文摘要
We introduce group-valued coloured interchange processes, a class of continuous-time random walks on wreath products generated by transpositions and arbitrary symmetric base-group transitions. We give a complete representation-theoretic characterisation of their spectral gaps by decomposing the associated quasi-regular representation and determining precisely which irreducible representations are required. For abelian base groups, we realise these representations on multislices and identify their Laplacians with discrete Schrödinger operators. We then classify the minimal families of irreducible representations that determine the spectral gap for every choice of transition rates.
Comments13 pages
