Research Paper#Mathematics, Probability, Markov Chains, Combinatorics🔬 ResearchAnalyzed: Jan 3, 2026 17:14
k-Plancherel Measure and Finite Markov Chain
Published:Dec 30, 2025 16:57
•1 min read
•ArXiv
Analysis
This paper explores the $k$-Plancherel measure, a generalization of the Plancherel measure, using a finite Markov chain. It investigates the behavior of this measure as the parameter $k$ and the size $n$ of the partitions change. The study is motivated by the connection to $k$-Schur functions and the convergence to the Plancherel measure. The paper's significance lies in its exploration of a new growth process and its potential to reveal insights into the limiting behavior of $k$-bounded partitions.
Key Takeaways
- •Introduces a growth process on $k$-cores whose stationary distribution is the $k$-Plancherel measure.
- •Connects the $k$-Plancherel measure to a finite Markov chain with $k!$ states.
- •Conjectures about the limiting behavior of the measure as $n$ approaches infinity for fixed $k$.
- •Initiates the study of these processes and presents theorems and conjectures.
Reference
“The paper initiates the study of these processes, state some theorems and several intriguing conjectures found by computations of the finite Markov chain.”