Central measures on the r-differential version of the Young--Fibonacci graph

TL;DR

This paper characterizes the Martin boundary and ergodic measures of the path space associated with the r-differential Young--Fibonacci graph, advancing understanding of its probabilistic and combinatorial structure.

Contribution

It introduces the Martin boundary and ergodic measures for the r-differential Young--Fibonacci graph's path space, a novel extension in this area.

Findings

Martin boundary of the r-differential Young--Fibonacci graph's path space described.

Ergodicity of the associated measures established.

Provides foundational results for probabilistic analysis of the graph.

Abstract

We describe Martin boundary of the path space of $r$-differential version of Young--Fibonacci graph. Also we establish ergodicity of the corresponding measures.