Matrix models for random partitions
Copyright policy )Matrix models for random partitions
We derive exact matrix integral representations for different sums over partitions. The characteristic feature of all obtained matrix models is the presence of logarithmic (or, vice versa, exponential) terms in the potential. Our derivation is based on the application of the higher Casimir operators. The Toda lattice integrability of the basic sums over partitions can be easily derived from the matrix model representation.
26 pages, presentation improved, references corrected
- École Normale Supérieure France
- Institut de Biologie - l'Ecole Normale Supérieure France
- Ecole Normale Supérieure France
- Ecole Normale Supérieure France
- ECOLE NORMALE SUPERIEURE France
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Applications of Lie groups to the sciences; explicit representations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Mathematical Physics (math-ph), Mathematical Physics
High Energy Physics - Theory, High Energy Physics - Theory (hep-th), Applications of Lie groups to the sciences; explicit representations, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), FOS: Physical sciences, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Mathematical Physics (math-ph), Mathematical Physics
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