论文标题
与离散贝塞尔点过程的有限温度变形相关的集成方程
Integrable equations associated with the finite-temperature deformation of the discrete Bessel point process
论文作者
论文摘要
我们研究离散贝塞尔点过程的有限温度变形。我们表明，其最大的粒子分布满足了2d TODA方程的减少，并且是Amir-Corwin-quastel的多数差异性PainlevéII等方程的离散版本，我们计算了在betea和Betea和Bouttier证明的Poissonization参数的初始条件，并在适当的粒子分配中限制了量相当的限制。我们表明，2D TODA方程的降低减少到Korteweg-de Vries方程，以及离散的integro-differendentiven-differentialPainlevéII方程将其连续版本降低。我们的方法基于Borodin和Deift开发的ITS-izergin-Korepin-Slavnov理论的离散类似物。
We study the finite-temperature deformation of the discrete Bessel point process. We show that its largest particle distribution satisfies a reduction of the 2D Toda equation, as well as a discrete version of the integro-differential Painlevé II equation of Amir-Corwin-Quastel, and we compute initial conditions for the Poissonization parameter equal to 0. As proved by Betea and Bouttier, in a suitable continuum limit the last particle distribution converges to that of the finite-temperature Airy point process. We show that the reduction of the 2D Toda equation reduces to the Korteweg-de Vries equation, as well as the discrete integro-differential Painlevé II equation reduces to its continuous version. Our approach is based on the discrete analogue of Its-Izergin-Korepin-Slavnov theory of integrable operators developed by Borodin and Deift.
