5 citations · 8 across the 4 of their papers we have counts for
4 papers
Total positivity and spectral theory for Toeplitz Hessenberg matrix ensembles
Nicholas Ercolani, John Peca-Medlin, Jonathan Ramalheira-Tsu
In this paper we define and lay the groundwork for studying a novel matrix ensemble: totally positive Hessenberg Toeplitz operators, denoted TPHT. This is the intersection of two e…
Lusztig Factorization Dynamics of the Full Kostant-Toda Lattices
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
We study extensions of the classical Toda lattices at several different space-time scales. These extensions are from the classical tridiagonal phase spaces to the phase space of fu…
A Path-Counting Analysis of Phase Shifts in Box-Ball Systems
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
In this paper, we perform a detailed analysis of the phase shift phenomenon of the classical soliton cellular automaton known as the box-ball system, ultimately resulting in a stat…
The Ghost-Box-Ball System: A Unified Perspective on Soliton Cellular Automata, the RSK Algorithm and Phase Shifts
Nicholas M. Ercolani, Jonathan Ramalheira-Tsu
In this paper, we introduce the ghost-box-ball system, which is an extended version of the classical soliton cellular automaton. It is initially motivated as a mechanism for making…