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作者：Simmons, David; Weiss, Barak
作者单位：University of York - UK; Tel Aviv University
摘要：We extend results of Y. Benoist and J.-F. Quint concerning random walks on homogeneous spaces of simple Lie groups to the case where the measure defining the random walk generates a semigroup which is not necessarily Zariski dense, but satisfies some expansion properties for the adjoint action. Using these dynamical results, we study Diophantine properties of typical points on some self-similar fractals in R-d. As examples, we show that for any self-similar fractal K subset of R-d satisfying t...
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作者：Montgomery, Richard
作者单位：University of California System; University of California Santa Cruz
摘要：For the Newtonian 4-body problem in space we prove that any zero angular momentum bounded solution suffers infinitely many coplanar instants, that is, times at which all 4 bodies lie in the same plane. This result generalizes a known result for collinear instants (syzygies) in the zero angular momentum planar 3-body problem, and extends to thed + 1 body problem in d-space. The proof begins by identifying the translation-reduced configuration space with real dxd matrices, the degeneration locus...
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作者：Blair, Matthew D.; Sogge, Christopher D.
作者单位：University of New Mexico; Johns Hopkins University
摘要：We consider the problem of proving Lp bounds for eigenfunctions of the Laplacian in the high frequency limit in the presence of nonpositive curvature and more generally, manifolds without conjugate points. In particular, we prove estimates at the critical exponent pc=2(d+1)d-1, where a spectrum of scenarios for phase space concentration must be ruled out. Our work establishes a gain of an inverse power of the logarithm of the frequency in the bounds relative to the classical Lp bounds of the s...
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作者：Aizenman, Michael; Duminil-Copin, Hugo; Tassion, Vincent; Warzel, Simone
作者单位：Princeton University; Universite Paris Saclay; University of Geneva; Swiss Federal Institutes of Technology Domain; ETH Zurich; Technical University of Munich
摘要：The known Pfaffian structure of the boundary spin correlations, and more generally order-disorder correlation functions, is given a new explanation through simple topological considerations within the model's random current representation. This perspective is then employed in the proof that the Pfaffian structure of boundary correlations emerges asymptotically at criticality in Ising models on Z2 with finite-range interactions. The analysis is enabled by new results on the stochastic geometry ...
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作者：Sidoravicius, Vladas; Stauffer, Alexandre
作者单位：New York University; NYU Shanghai; University of Bath; Roma Tre University
摘要：We consider a stochastic aggregation model on Z(d). Start with particles distributed according to the product Bernoulli measure with parameter mu. In addition, start with an aggregate at the origin. Non-aggregated particles move as continuous-time simple random walks obeying the exclusion rule, whereas aggregated particles do not move. The aggregate grows by attaching particles to its surface whenever a particle attempts to jump onto it. This evolution is called multi-particle diffusion limite...
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作者：Beliakova, Anna; Putyra, Krzysztof K.; Wehrli, Stephan M.
作者单位：University of Zurich; Syracuse University
摘要：Motivated by topology, we develop a general theory of traces and shadows for an endobicategory, which is a pair: bicategory and endobifunctor . For a graded linear bicategory and a fixed invertible parameter q, we quantize this theory by using the endofunctor sigma q such that sigma q:=q-deg sigma for any 2-morphism and coincides with sigma otherwise. Applying the quantized trace to the bicategory of Chen-Khovanov bimodules we get a new triply graded link homology theory called quantum annular...
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作者：Frohman, Charles; Kania-Bartoszynska, Joanna; Le, Thang
作者单位：University of Iowa; National Science Foundation (NSF); University System of Georgia; Georgia Institute of Technology
摘要：This paper resolves the unicity conjecture of Bonahon and Wong for the Kauffman bracket skein algebras of all oriented finite type surfaces at all roots of unity. The proof is a consequence of a general unicity theorem that says that the irreducible representations of a prime affine k-algebra over an algebraically closed field k, that is finitely generated as a module over its center, are generically classified by their central characters. The center of the Kauffman bracket skein algebra of an...
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作者：Seward, Brandon
作者单位：New York University
摘要：For an ergodic p.m.p. action G?(X,) of a countable group G, we define the Rokhlin entropy hGRok(X,) to be the infimum of the Shannon entropies of countable generating partitions. It is known that for free ergodic actions of amenable groups this notion coincides with classical Kolmogorov-Sinai entropy. It is thus natural to view Rokhlin entropy as a close analogue to classical entropy. Under this analogy we prove that Krieger's finite generator theorem holds for all countably infinite groups. S...
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作者：Goldring, Wushi; Koskivirta, Jean-Stefan
作者单位：Stockholm University; University of Tokyo
摘要：We construct group-theoretical generalizations of the Hasse invariant on strata closures of the stacks G-Zip(mu). Restricting to zip data of Hodge type, we obtain a group-theoretical Hasse invariant on every Ekedahl-Oort stratum closure of a general Hodge-type Shimura variety. A key tool is the construction of a stack of zip flags G-ZipFlag(mu), fibered in flag varieties over G-Zip(mu). It provides a simultaneous generalization of the classical case homogeneous complex manifolds studied by Gri...
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作者：Berger, Pierre
作者单位：Universite Paris 13
