Conditional measures of determinantal point processes

An explicit description is given for conditional measures of determinantal point processes corresponding to integrable kernels in one dimension, including those corresponding to de Branges spaces (joint work with Tomoyuki Shirai), as well as to kernels of orthogonal projection onto generalized Fock spaces (joint work with Yanqi Qiu). The main result is that the conditional measure of our process in a bounded domain with respect to the fixed configuration in the exterior is an orthogonal polynomial ensemble with explicitly found weight. For Bergman spaces in bounded domains, in joint work with Shilei Fan and Yanqi Qiu, it is shown that the determinantal point process is equivalent to its reduced Palm measures.

References

58. A. I. Bufetov, “Ierarkhiya Palma dlya determinantnykh tochechnykh protsessov s yadrom Besselya”, Tr. MIAN, 297, 2017, 105–112        ; A. I. Bufetov, “A Palm Hierarchy for Determinantal Point Processes with the Bessel Kernel”, Proc. Steklov Inst. Math., 297 (2017), 90–97        
59. A. I. Bufetov, S. Fan, Y. Qiu, Y., “Equivalence of Palm measures for determinantal point processes governed by Bergman kernels”, Probab. Theory Relat. Fields, 2017 (to appear)  
60. A. I. Bufetov, “Quasi-Symmetries of Determinantal Point Processes.”, Annals of Probability (to appear) http://www.imstat.org/aop/future_papers.htm
61. A. I. Bufetov, Tomoyuki Shirai, “Quasi-symmetries and rigidity for determinantal point processes associated with de Branges spaces”, Proc. Japan Acad. Ser. A Math. Sci., 93:1 (2017), 1–5        
62. Alexander I. Bufetov, Yanqi Qiu, “Conditional measures of generalized Ginibre point processes”, J. Funct. Anal., 272:11 (2017), 4671–4708