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作者：Chaika, Jon
摘要：We show that every transformation is disjoint from almost every interval exchange transformation (JET), answering a question of Bufetov. In particular, we prove that almost every pair of IETs is disjoint. It follows that the product of almost every pair is uniquely ergodic. A key step in the proof is showing that any sequence of density 1 contains a rigidity sequence for almost every JET, strengthening a result of Veech.
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作者：Li, Hanfeng
摘要：For a countable amenable group F and an element f in the integral group ring Z Gamma being invertible in the group von Neumann algebra of Gamma, we show that the entropy of the shift action of F on the Pontryagin dual of the quotient of Z Gamma by its left ideal generated by f is the logarithm of the Fuglede-Kadison determinant of f. For the proof, we establish an l(P)-version of Rufus Bowen's definition of topological entropy, addition formulas for group extensions of countable amenable group...
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作者：Green, Ben; Tao, Terence; Ziegler, Tamar
摘要：We prove the inverse conjecture for the Gowers Us+1[N]-norm for all s >= 1; this is new for s >= 4. More precisely, we establish that if f : [N] -> [-1, 1] is a function with parallel to f parallel to(Us+1) ([N]) >= delta, then there is a bounded-complexity s-step nilsequence F(g(n)Gamma) that correlates with f, where the bounds on the complexity and correlation depend only on s and delta. From previous results, this conjecture implies the Hardy-Littlewood prime tuples conjecture for any linea...
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作者：Hochman, Michael; Shmerkin, Pablo
摘要：We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of self-similarity under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We apply this to prove the following conjecture of Furstenberg: if X, Y subset of [0, 1] are closed and invariant, respectively, under xm mod 1 and xn mod 1, where m, n are not powers of the same integer, then, for any t not equal 0, dim(X + tY) = min{1, dim X + dim ...
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作者：Wastlund, Johan
摘要：We establish the soundness of the replica symmetric ansatz introduced by M. Mezard and G. Parisi for the minimum matching problem in the pseudo-dimension d mean field model for d >= 1. The case d = 1 corresponds to the pi(2)/6-limit for the assignment problem proved by D. Aldous in 2001. We introduce a game-theoretical framework by which we establish the analogous limit also for d > 1.
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作者：Green, Ben; Tao, Terence
摘要：We show that the Mobius function mu(n) is strongly asymptotically orthogonal to any polynomial nilsequence (F(g(n)Gamma))(n is an element of N). Here, G is a simply-connected nilpotent Lie group with a discrete and cocompact subgroup F (so G/Gamma is a nilmanifold), g : Z -> G is a polynomial sequence, and F : G/Gamma -> R is a Lipschitz function. More precisely, we show that vertical bar 1/N Sigma(N)(n=1),mu(n)F(g(n)Gamma)vertical bar <<(F,G,Gamma,A) log(-A) N for all A > 0. In particular, th...
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作者：Shelstad, D.
摘要：We prove the existence of a transfer of orbital integrals in endoscopy for real reductive groups when there is twisting by an automorphism defined over the reals and by a character on the real points of the group. Our proof contains a relatively short self-contained argument for the already known case of standard endoscopy.
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作者：Berthelot, Pierre; Esnault, Helene; Ruelling, Kay
摘要：Let R be a discrete valuation ring of mixed characteristics (0, p), with finite residue field k and fraction field K, let k' be a finite extension of k, and let X be a regular, proper and flat R-scheme, with generic fibre X-K and special fibre X-k. Assume that X-K is geometrically connected and of Hodge type >= 1 in positive degrees. Then we show that the number of k'-rational points of X satisfies the congruence vertical bar X(k')vertical bar equivalent to 1 mod vertical bar k'vertical bar. W...
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作者：Hatami, Hamed
摘要：We show that on every product probability space, Boolean functions with small total influences are essentially the ones that are almost measurable with respect to certain natural sub-sigma algebras. This theorem in particular describes the structure of monotone set properties that do not exhibit sharp thresholds. Our result generalizes the core of Friedgut's seminal work on properties of random graphs to the setting of arbitrary Boolean functions on general product probability spaces and impro...
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作者：Buff, Xavier; Cheritat, Arnaud
摘要：We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure. We find such examples with a Cremer fixed point, with a Siegel disk, or with infinitely many satellite renormalizations.
