For q-deformed bipartite planar maps, boundary geodesic chord diagrams are distributed exactly as in the double-scaled SYK model, with weights depending only on crossing number.
The askey-scheme of hyperge- ometric orthogonal polynomials and its q-analogue
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abstract
We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal polynomials in this scheme. In chapeter 2 we give all limit relation between different classes of orthogonal polynomials listed in the Askey-scheme. In chapter 3 we list the q-analogues of the polynomials in the Askey-scheme. We give their definition, orthogonality relation, three term recurrence relation and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally in chapter 5 we point out how the `classical` hypergeometric orthogonal polynomials of the Askey-scheme can be obtained from their q-analogues.
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The optimal input signal state for minimizing detectability in sparse covert signaling over bosonic channels is a mixture of two consecutive photon-number states, specifically vacuum and single photon in low-brightness regime.
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Double-scaled SYK from boundary metrics of planar maps
For q-deformed bipartite planar maps, boundary geodesic chord diagrams are distributed exactly as in the double-scaled SYK model, with weights depending only on crossing number.
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Covert Signaling for Communication and Sensing over the Bosonic Channels
The optimal input signal state for minimizing detectability in sparse covert signaling over bosonic channels is a mixture of two consecutive photon-number states, specifically vacuum and single photon in low-brightness regime.