Finiteness of Transformation Groups in Multidimensional Orthant Walks

This paper addresses a fundamental question in the study of random walks confined to multidimensional spaces. The finiteness of a specific group of transformations is crucial for applying techniques to compute generating functions, which are essential for analyzing these walks. The paper provides new results on characterizing the conditions under which this group is finite, offering valuable insights for researchers working on these types of problems. The complete characterization in 2D and the constraints on higher dimensions are significant contributions.

• •Provides a complete characterization of finite groups in 2D.
• •Shows that finite groups in higher dimensions must be isomorphic to simpler reflection groups.
• •Offers a full classification of parameters leading to a finite group with a Weyl property in 3D.