schur process
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2019 ◽  
Vol 2020 (20) ◽  
pp. 6713-6768
Author(s):  
Alexei Borodin ◽  
Vadim Gorin ◽  
Eugene Strahov

AbstractWe consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of squared singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.


2018 ◽  
Vol 19 (12) ◽  
pp. 3663-3742 ◽  
Author(s):  
Dan Betea ◽  
Jérémie Bouttier ◽  
Peter Nejjar ◽  
Mirjana Vuletić
Keyword(s):  

2015 ◽  
Vol 30 (33) ◽  
pp. 1550202 ◽  
Author(s):  
Amer Iqbal ◽  
Babar A. Qureshi ◽  
Khurram Shabbir ◽  
Muhammad A. Shehper

We study (p, q) 5-brane webs dual to certain N M5-brane configurations and show that the partition function of these brane webs gives rise to cylindric Schur process with period N. This generalizes the previously studied case of period 1. We also show that open string amplitudes corresponding to these brane webs are captured by the generating function of cylindric plane partitions with profile determined by the boundary conditions imposed on the open string amplitudes.


2011 ◽  
Vol 844 (2) ◽  
pp. 334-347 ◽  
Author(s):  
Amer Iqbal ◽  
Can Kozçaz ◽  
Tanweer Sohail
Keyword(s):  

2007 ◽  
Vol 140 (3) ◽  
pp. 391-468 ◽  
Author(s):  
Alexei Borodin
Keyword(s):  

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