k-Plancherel Measure and Finite Markov Chain
Research Paper#Mathematics, Probability, Markov Chains, Combinatorics🔬 Research|Analyzed: Jan 3, 2026 17:14•
Published: Dec 30, 2025 16:57
•1 min read
•ArXivAnalysis
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 / Citation
View Original"The paper initiates the study of these processes, state some theorems and several intriguing conjectures found by computations of the finite Markov chain."