Spectral theory for the q-Boson particle system

被引:31
|
作者
Borodin, Alexei [1 ,2 ]
Corwin, Ivan [1 ,3 ,4 ]
Petrov, Leonid [2 ,5 ]
Sasamoto, Tomohiro [6 ,7 ]
机构
[1] MIT, Dept Math, Cambridge, MA 02139 USA
[2] Inst Informat Transmiss Problems, Moscow 127994, Russia
[3] Columbia Univ, Dept Math, New York, NY 10027 USA
[4] Clay Math Inst, Providence, RI 02903 USA
[5] Northeastern Univ, Dept Math, Boston, MA 02115 USA
[6] Chiba Univ, Dept Math, Inage Ku, Chiba 2638522, Japan
[7] Tech Univ Munich, Zentrum Math, D-85748 Garching, Germany
基金
美国国家科学基金会;
关键词
Bethe ansatz; Plancherel theory; quantum integrable systems; q-Boson; FREE-ENERGY FLUCTUATIONS; PLANCHEREL DECOMPOSITION; DIRECTED POLYMERS; BODY PROBLEM; FORMULA; GAS; DIAGONALIZATION; REPRESENTATION; PROBABILITY; EQUATION;
D O I
10.1112/S0010437X14007532
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We develop spectral theory for the generator of the q-Boson (stochastic) particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem has various implications. It proves the completeness of the Bethe ansatz for the q-Boson generator and consequently enables us to solve the Kolmogorov forward and backward equations for general initial data. Owing to a Markov duality with q-TASEP (q-deformed totally asymmetric simple exclusion process), this leads to moment formulas which characterize the fixed time distribution of q-TASEP started from general initial conditions. The theorem also implies the biorthogonality of the left and right eigenfunctions. We consider limits of our q-Boson results to a discrete delta Bose gas considered previously by van Diejen, as well as to another discrete delta Bose gas that describes the evolution of moments of the semi-discrete stochastic heat equation (or equivalently, the O'Connell-Yor semi-discrete directed polymer partition function). A further limit takes us to the delta Bose gas which arises in studying moments of the stochastic heat equation/Kardar-Parisi-Zhang equation.
引用
收藏
页码:1 / 67
页数:67
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