Permanental Processes with Kernels That Are Not Equivalent to a Symmetric Matrix

  • Michael B. MarcusEmail author
  • Jay Rosen
Conference paper
Part of the Progress in Probability book series (PRPR, volume 74)


Kernels of α-permanental processes of the form

$$\displaystyle \begin{aligned} \widetilde u(x,y)=u(x,y)+f(y),\qquad x,y\in S, \end{aligned} $$

which u(x, y) is symmetric, and f is an excessive function for the Borel right process with potential densities u(x, y), are considered. Conditions are given that determine whether \(\{\widetilde u(x,y);x,y\in S\}\) is symmetrizable or asymptotically symmetrizable.


Permanental processes Symmetrizable 

AMS 2010 Subject Classification

60K99 60J25 60J27 60G15 60G99 



Research of Jay Rosen was partially supported by a grant from the Simons Foundation.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.CUNY Graduate CenterNew YorkUSA
  2. 2.Department of MathematicsCollege of Staten Island, CUNYStaten IslandUSA

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