| 1. |
- Ahlberg, Daniel, 1982, et al.
(författare)
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Noise sensitivity in continuum percolation
- 2014
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 201:2, s. 847-899
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the Poisson Boolean model, also known as the Gilbert disc model, is noise sensitive at criticality. This is the first such result for a Continuum Percolation model, and the first which involves a percolation model with critical probability pc not equal 1/2. Our proof uses a version of the Benjamini-Kalai-Schramm Theorem for biased product measures. A quantitative version of this result was recently proved by Keller and Kindler. We give a simple deduction of the non-quantitative result from the unbiased version. We also develop a quite general method of approximating Continuum Percolation models by discrete models with pc bounded away from zero; this method is based on an extremal result on non-uniform hypergraphs.
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| 2. |
- Balletti, Gabriele, et al.
(författare)
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Universal inequalities in Ehrhart theory
- 2018
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 227:2, s. 843-859
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we show the existence of universal inequalities for the h*-vector of a lattice polytope P, that is, we show that there are relations among the coefficients of the h*-polynomial that are independent of both the dimension and the degree of P. More precisely, we prove that the coefficients h* (1) and h* (2) of the h*-vector (h* (0), h* (1),..., h* (d) ) of a lattice polytope of any degree satisfy Scott's inequality if h* (3) = 0.
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| 3. |
- Berglund, Alexander, et al.
(författare)
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Homotopical Morita theory for corings
- 2018
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 227:1, s. 239-287
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Tidskriftsartikel (refereegranskat)abstract
- A coring (A,C) consists of an algebra A in a symmetric monoidal category and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings (A,C) and (B,D) in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules V (C)(A) and V (D)(B) are Quillen equivalent. As an illustration of the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.
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| 4. |
- Billig, Yuly, et al.
(författare)
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Representations of Lie algebras of vector fields on affine varieties
- 2019
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 1565-8511 .- 0021-2172. ; 233:1, s. 379-399
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Tidskriftsartikel (refereegranskat)abstract
- For an irreducible affine variety X over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on X—gauge modules and Rudakov modules, which admit a compatible action of the algebra of functions. Gauge modules are generalizations of modules of tensor densities whose construction was inspired by non-abelian gauge theory. Rudakov modules are generalizations of a family of induced modules over the Lie algebra of derivations of a polynomial ring studied by Rudakov [23]. We prove general simplicity theorems for these two types of modules and establish a pairing between them.
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| 5. |
- Björklund, Michael, 1981, et al.
(författare)
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Quasi-state rigidity for finite-dimensional Lie algebras
- 2017
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 221:1, s. 25-57
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Tidskriftsartikel (refereegranskat)abstract
- © 2017, Hebrew University of Jerusalem. We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C n ⋊ u(n), n ≥ 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimension ≤ 3 and for solvable Lie algebras which split over a codimension one abelian ideal, we show that this is the only obstruction to rigidity.
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| 6. |
- Björklund, Michael, 1981
(författare)
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Random walks on countable groups
- 2017
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 1565-8511 .- 0021-2172. ; 217:1, s. 371-382
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Tidskriftsartikel (refereegranskat)abstract
- We begin by giving a new proof of the equivalence between the Liouville property and vanishing of the drift for symmetric random walks with finite first moments on finitely generated groups; a result which was first established by Kaimanovich-Vershik and Karlsson-Ledrappier. We then proceed to prove that the product of the Poisson boundary of any countable measured group (G,mu) with any ergodic (G,mu)-space is still ergodic, which in particular yields a new proof of weak mixing for the double Poisson boundary of (G,mu) when mu is symmetric. Finally, we characterize the failure of weak-mixing for an ergodic (G,mu)-space as the existence of a non-trivial measure-preserving isometric factor.
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| 7. |
- Björner, Anders, et al.
(författare)
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ON SEQUENTIALLY COHEN-MACAULAY COMPLEXES AND POSETS
- 2009
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 169:1, s. 295-316
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Tidskriftsartikel (refereegranskat)abstract
- The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for posets is given. Finally, in an appendix we outline connections with ring-theory and survey some uses of sequential Cohen-Macaulayness in commutative algebra.
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| 8. |
- Bogart, Tristram, et al.
(författare)
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Finitely many smooth d-polytopes with n lattice points
- 2015
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Ingår i: Israel Journal of Mathematics. - : Springer Science and Business Media LLC. - 0021-2172 .- 1565-8511. ; 207:1, s. 301-329
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Tidskriftsartikel (refereegranskat)abstract
- We prove that for fixed n there are only finitely many embeddings of ℚ-factorial toric varieties X into ℙ n that are induced by a complete linear system. The proof is based on a combinatorial result that implies that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with ≤ 12 lattice points.
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| 9. |
- Bränden, Petter, 1976-, et al.
(författare)
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Lower bounds for contingency tables via Lorentzian polynomials
- 2023
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Ingår i: Israel Journal of Mathematics. - : Springer Nature. - 0021-2172 .- 1565-8511. ; 253:1, s. 43-90
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Tidskriftsartikel (refereegranskat)abstract
- We present a new lower bound on the number of contingency tables, improving upon and extending previous lower bounds by Barvinok [Bar09, Bar16] and Gurvits [Gur15]. As an application, we obtain new lower bounds on the volumes of flow and transportation polytopes. Our proofs are based on recent results on Lorentzian polynomials.
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| 10. |
- Coulembier, Kevin, et al.
(författare)
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Dualities and derived equivalences for category O
- 2017
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Ingår i: Israel Journal of Mathematics. - : HEBREW UNIV MAGNES PRESS. - 0021-2172 .- 1565-8511. ; 219:2, s. 661-706
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Tidskriftsartikel (refereegranskat)abstract
- We determine the Ringel duals for all blocks in the parabolic versions of the BGG category associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary to the original category and the specific previously known cases in the parabolic setting, the blocks are not necessarily Ringel self-dual. However, the parabolic category as a whole is still Ringel self-dual. Furthermore, we use generalisations of the Ringel duality functor to obtain large classes of derived equivalences between blocks in parabolic and original category . We subsequently classify all derived equivalence classes of blocks of category in type A which preserve the Koszul grading.
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