从Pearcey到Airy过程的间隙概率之间的过渡; Riemann-Hilbert方法
The transition between the gap probabilities from the Pearcey to the Airy process; a Riemann-Hilbert approach
摘要：
我们考虑的差距概率的Pearcey和Airy过程，我们建立了一个黎曼-希尔伯特方法（不同于标准的），从而大间隙/大时间的Pearcey过程的渐近分析示出因式分解成两个独立的Airy过程使用Deift-Zhou最陡下降分析。此外，我们还将可积核的Fredholm行列式理论与等单道τ函数理论联系起来。利用上面提到的Riemann-Hilbert问题，我们构造了一个合适的拉克斯对形式的Pearcey间隙概率和重新推导最近发现的两个非线性偏微分方程，并找到第三个不可约的。
英文摘要：
We consider the gap probability for the Pearcey and Airy processes; we set up a Riemann--Hilbert approach (different from the standard one) whereby the asymptotic analysis for large gap/large time of the Pearcey process is shown to factorize into two independent Airy processes using the Deift-Zhou steepest descent analysis. Additionally we relate the theory of Fredholm determinants of integrable kernels and the theory of isomonodromic tau function. Using the Riemann-Hilbert problem mentioned above we construct a suitable Lax pair formalism for the Pearcey gap probability and re-derive the two nonlinear PDEs recently found and additionally find a third one not reducible to those.
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