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Abstract: We study global fluctuations for singular values of M-fold products of several rightunitarily invariant N × N random matrix ensembles. As N → ∞, we show the fluctuations of their height functions converge to an explicit Gaussian field, which is log-correlated for M fixed and has a white noise component for M → ∞ jointly with N. Our technique centers on the study of the multivariate Bessel generating functions of these spectral measures, for which we prove a central limit theorem for global fluctuations via certain conditions on the generating functions. We apply our approach to a number of ensembles, including square roots of Wishart, Jacobi, and unitarily invariant positive definite matrices with fixed spectrum ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: Recently James Martin introduced multiline queues, and used them to give a combinatorial formula for the stationary distribution of the multispecies asymmetric simple exclusion process (ASEP) on a circle. The ASEP is a model of particles hopping on a one-dimensional lattice, which was introduced around 1970, and has been extensively studied in statistical mechanics, probability, and combinatorics. In this article we give an independent proof of Martin's result, and we show that by introducing additional statistics on multiline queues, we can use them to give a new combinatorial formula for both the symmetric Macdonald polynomials Pλ(x;q,t), and the nonsymmetric Macdonald polynomials Eλ(x;q,t), where λ is a ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: We settle several long-standing problems in the theory of cyclotomic Hecke algebras: for each charge we construct the integral cellular basis predicted by Ariki's categorification theorem. We hence prove unitriangularity of decomposition matrices and Martin–Woodcock's ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: We use the theory of foliations to study the relative canonical divisor of a normalized inseparable base-change. Our main technical theorem states that it is linearly equivalent to a divisor with positive integer coefficients divisible by p − 1. We deduce many consequences about the fibrations of the minimal model program: for example the general fibers of terminal Mori fiber spaces of relative dimension 2 are normal in characteristic p ≥ 5 and smooth in characteristic p ≥ ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: We study closed ancient solutions to gradient flows of elliptic functionals in Riemannian manifolds, including mean curvature flow and harmonic map heat flow. Our work has various consequences. In all dimensions and codimensions, we classify ancient mean curvature flows in Sn with low area: they are steady or shrinking equatorial spheres. In the mean curvature flow case in S3, we classify ancient flows with more relaxed area bounds: they are steady or shrinking equators or Clifford tori. In the embedded curve shortening case in S2, we completely classify ancient flows of bounded length: they are steady or shrinking ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: We study the complexity of birational self-maps of a projective threefold X by looking at the birational type of surfaces contracted. These surfaces are birational to the product of the projective line with a smooth projective curve. We prove that the genus of the curves occuring is unbounded if and only if X is birational to a conic bundle or a fibration into cubic surfaces. Similarly, we prove that the gonality of the curves is unbounded if and only if X is birational to a conic ... Read More PubDate: 2022-03-19T00:00:00-05:00
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Abstract: For almost all Riemannian metrics (in the C∞ Baire sense) on a compact manifold with boundary (Mn+1, ∂M), 3 ≤ (n + 1) ≤ 7, we prove that, for any open subset V of ∂M, there exists a compact, properly embedded free boundary minimal hypersurface intersecting ... Read More PubDate: 2022-03-19T00:00:00-05:00
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