Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fluctuations of $\beta$-Jacobi Product Processes   We study Markov chains formed by squared singular values of products of
truncated orthogonal, unitary, symplectic matrices (corresponding to the Dyson
index $\beta = 1,2,4$ respectively) where time corresponds to the number of
terms in the product. More generally, we consider the $\beta$-Jacobi product
process obtained by extrapolating to arbitrary $\beta > 0$. When the time
scaling is preserved, we show that the global fluctuations are jointly Gaussian
with explicit covariances. For time growing linearly with matrix size, we show
convergence of moments after suitable rescaling. When $\beta = 2$, our results
imply that the right edge converges to a process which interpolates between the
Airy point process and a deterministic configuration. This process connects a
time-parametrized family of point processes appearing in the works of
Akemann-Burda-Kieburg and Liu-Wang-Wang across time. In the arbitrary $\beta >
0$ case, our results show tightness of the particles near the right edge. The
limiting moment formulas correspond to expressions for the Laplace transform of
a conjectural $\beta$-generalization of the interpolating process.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org