Geometric RSK and the Toda lattice
From MaRDI portal
Publication:470867
zbMath1325.37047arXiv1308.4631MaRDI QIDQ470867
Publication date: 13 November 2014
Published in: Illinois Journal of Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1308.4631
Brownian motionToda latticesemi-classical limitquantum Toda latticegeometric Robinson-Schensted-Knuth correspondence
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Interacting random processes; statistical mechanics type models; percolation theory (60K35)
Related Items
A path-counting analysis of phase shifts in box-ball systems, Discrete Whittaker processes, The Poisson geometry of Plancherel formulas for triangular groups, Lusztig factorization dynamics of the full Kostant-Toda lattices, Stochastic Bäcklund Transformations, Interacting diffusions on positive definite matrices, The ghost-box-ball system: a unified perspective on soliton cellular automata, the RSK algorithm and phase shifts, Dualities in quantum integrable many-body systems and integrable probabilities. I., Interlacing networks: birational RSK, the octahedron recurrence, and Schur function identities
Cites Work
- Unnamed Item
- Directed polymers and the quantum Toda lattice
- Alternating-sign matrices and domino tilings. II
- Geometric RSK correspondence, Whittaker functions and symmetrized random polymers
- Strong stationary times via a new form of duality
- Littelmann paths and Brownian paths
- Singular structure of Toda lattices and cohomology of certain compact Lie groups
- New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
- On the shuffling algorithm for domino tilings
- Continuous crystal and Duistermaat-Heckman measure for Coxeter groups.
- Large time asymptotics of growth models on space-like paths. I: Push ASEP
- Some examples of dynamics for Gelfand-tsetlin patterns
- Binomial determinants, paths, and hook length formulae
- The solution to a generalized Toda lattice and representation theory
- Generalized domino-shuffling.
- Toda lattices with indefinite metric. II: Topology of the iso-spectral manifolds
- A representation for non-colliding random walks
- Paths in Weyl chambers and random matrices
- Parametrizations of canonical bases and totally positive matrices
- Exponential functionals of Brownian motion and class-one Whittaker functions
- Tropical combinatorics and Whittaker functions
- Macdonald processes
- Dyson's Brownian motions, intertwining and interlacing
- Random walks in Weyl chambers and crystals
- On a Gauss-Givental representation of quantum Toda chain wave function
- One-dimensional Brownian motion and the three-dimensional Bessel process
- Double Bruhat cells and total positivity
- On the distribution of the length of the longest increasing subsequence of random permutations
- A version of Pitman's 2M — X theorem for geometric Brownian motions
- A path-transformation for random walks and the Robinson-Schensted correspondence
- Conditioned random walks and the RSK correspondence
- Limit theorems for height fluctuations in a class of discrete space and time growth models
