Gap Probabilities for the Generalized Bessel Process: A Riemann-Hilbert Approach

作者：Girotti Manuela^*

来源：Mathematical Physics, Analysis and Geometry, 2014, 17(1-2): 183-211.

DOI：10.1007/s11040-014-9149-2

• Random point processes
• Gap probabilities
• Riemann-Hilbert problems
• Integrable kernels

We consider the gap probability for the Generalized Bessel process in the single-time and multi-time case, a determinantal process which arises as critical limiting kernel in the study of self-avoiding squared Bessel paths. We prove that such gap probabilities, i.e. the scalar and matrix Fredholm determinant of the process respectively, can be expressed in terms of determinants of suitable Its-Izergin-Korepin-Slavnov integrable kernels and therefore they can be related in a canonical way to Riemann-Hilbert problems. Moreover, such Fredholm determinants can be interpreted as isomonodromic tau-functions in the sense of Jimbo, Miwa and Ueno; in particular, in the single-time case we are able to construct an explicit Lax pair. On the other hand, in the multi-time case we explicitly define a completely new multi-time kernel and we proceed with the study of gap probabilities as in the single-time case.

• 出版日期2014-6