| 1. |
- Kruglyak, Natan, et al.
(författare)
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A distance between orbits that controls commutator estimates and invertibility of operators
- 2004
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Ingår i: Advances in Mathematics. - 0001-8708 .- 1090-2082. ; 182:1, s. 78-123
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Tidskriftsartikel (refereegranskat)abstract
- A distance between orbit spaces generated by a single element is introduced and it is shown that if an operator is invertible in one orbit it is also invertible in nearby orbits, thus proving a version of Shneiberg's theorem for orbital methods. The same machinery is used to extend the celebrated Rochberg-Weiss commutator theorem to the setting of orbital methods. It is shown that these results apply to the real and complex methods of interpolation by proving that these methods can be suitably obtained as orbits of a single element.
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| 2. |
- Abdallah, Nancy, et al.
(författare)
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Topology of posets with special partial matchings
- 2019
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Ingår i: Advances in Mathematics. - : Academic Press. - 0001-8708 .- 1090-2082. ; 348, s. 255-276
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Tidskriftsartikel (refereegranskat)abstract
- Special partial matchings (SPMs) are a generalisation of Brentis special matchings. Let a pircon be a poset in which every non-trivial principal order ideal is finite and admits an SPM. Thus pircons generalise Mariettis zircons. We prove that every open interval in a pircon is a PL ball or a PL sphere. It is then demonstrated that Bruhat orders on certain twisted identities and quasiparabolic W-sets constitute pircons. Together, these results extend a result of Can, Cherniaysky, and Twelbeck, prove a conjecture of Hultman, and confirm a claim of Rains and Vazirani.
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| 3. |
- Abouzaid, Mohammed, et al.
(författare)
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Monotone Lagrangians in cotangent bundles of spheres
- 2023
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Ingår i: Advances in Mathematics. - : Elsevier. - 0001-8708 .- 1090-2082. ; 427
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Tidskriftsartikel (refereegranskat)abstract
- We study the compact monotone Fukaya category of T*Sn, for n & GE; 2, and show that it is split-generated by two classes of objects: the zero-section Sn (equipped with suitable bounding cochains) and a 1-parameter family of monotone Lagrangian tori (S1 x Sn-1)& tau;, with monotonicity constants & tau; > 0 (equipped with rank 1 unitary local systems). As a consequence, any closed orientable spin monotone Lagrangian (possibly equipped with auxiliary data) with non-trivial Floer cohomology is non-displaceable from either Sn or one of the (S1 x Sn-1)& tau;. In the case of T*S3, the monotone Lagrangians (S1 x S2)& tau; can be replaced by a family of monotone tori T & tau;3.& COPY.
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| 4. |
- Adamowicz, Tomasz, et al.
(författare)
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Prime ends for domains in metric spaces
- 2013
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Ingår i: Advances in Mathematics. - : Elsevier. - 0001-8708 .- 1090-2082. ; 238, s. 459-505
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we propose a new definition of prime ends for domains in metric spaces under rather general assumptions. We compare our prime ends to those of Caratheodory and Nakki. Modulus ends and prime ends, defined by means of the p-modulus of curve families, are also discussed and related to the prime ends. We provide characterizations of singleton prime ends and relate them to the notion of accessibility of boundary points, and introduce a topology on the prime end boundary. We also study relations between the prime end boundary and the Mazurkiewicz boundary. Generalizing the notion of John domains, we introduce almost John domains, and we investigate prime ends in the settings of John domains, almost John domains and domains which are finitely connected at the boundary.
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| 5. |
- Adler, Mark, et al.
(författare)
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Double Aztec diamonds and the tacnode process
- 2014
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 252, s. 518-571
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Tidskriftsartikel (refereegranskat)abstract
- Discrete and continuous non-intersecting random processes have given rise to critical "infinite-dimensional diffusions", like the Airy process, the Pearcey process and variations thereof. It has been known that domino tilings of very large Aztec diamonds lead macroscopically to a disordered region within an inscribed ellipse (arctic circle in the homogeneous case), and a regular brick-like region outside the ellipse. The fluctuations near the ellipse, appropriately magnified and away from the boundary of the Aztec diamond, form an Airy process, run with time tangential to the boundary. This paper investigates the domino tiling of two overlapping Aztec diamonds; this situation also leads to non-intersecting random walks and an induced point process; this process is shown to be determinantal. In the large size limit, when the overlap is such that the two arctic ellipses for the single Aztec diamonds merely touch, a new critical process will appear near the point of osculation (tacnode), which is run with a time in the direction of the common tangent to the ellipses: this is the tacnode process. It is also-shown here that this tacnode process is universal: it coincides with the one found in the context of two groups of non-intersecting random walks or also Brownian motions, meeting momentarily.
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| 6. |
- Ahlberg, Daniel, et al.
(författare)
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Quenched Voronoi percolation
- 2016
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 286, s. 889-911
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the probability of crossing a large square in quenched Voronoi percolation converges to 1/2 at criticality, confirming a conjecture of Benjamini, Kalai and Schramm from 1999. The main new tools are a quenched version of the box-crossing property for Voronoi percolation at criticality, and an Efron Stein type bound on the variance of the probability of the crossing event in terms of the sum of the squares of the influences. As a corollary of the proof, we moreover obtain that the quenched crossing event at criticality is almost surely noise sensitive.
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| 7. |
- Alexandersson, Per, 1987-, et al.
(författare)
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A combinatorial expansion of vertical-strip LLT polynomials in the basis of elementary symmetric functions
- 2022
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 400
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Tidskriftsartikel (refereegranskat)abstract
- We give a new characterization of the vertical-strip LLT polynomials GP(x;q) as the unique family of symmetric functions that satisfy certain combinatorial relations. This characterization is then used to prove an explicit combinatorial expansion of vertical-strip LLT polynomials in terms of elementary symmetric functions. Such formulas were conjectured independently by A. Garsia et al. and the first named author, and are governed by the combinatorics of orientations of unit-interval graphs. The obtained expansion is manifestly positive if q is replaced by q+1, thus recovering a recent result of M. D'Adderio. Our results are based on linear relations among LLT polynomials that arise in the work of D'Adderio, and of E. Carlsson and A. Mellit. To some extent these relations are given new bijective proofs using colorings of unit-interval graphs. As a bonus we obtain a new characterization of chromatic quasisymmetric functions of unit-interval graphs.
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| 8. |
- Alfonseca, M Angeles, et al.
(författare)
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Analyticity of layer potentials and L-2 solvability of boundary value problems for divergence form elliptic equations with complex L-infinity coefficients
- 2011
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Ingår i: Advances in Mathematics. - : Elsevier Science B.V. Amsterdam. - 0001-8708 .- 1090-2082. ; 226:5, s. 4533-4606
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Tidskriftsartikel (refereegranskat)abstract
- We consider divergence form elliptic operators of the form L = -div A (x)del, defined in Rn+1 = {(x, t) is an element of R-n x R}, n andgt;= 2, where the L-infinity coefficient matrix A is (n + 1) x (n + 1), uniformly elliptic, complex and t-independent. We show that for such operators, boundedness and invertibility of the corresponding layer potential operators on L-2 (R-n) = L-2(partial derivative R-+(n+1)) is stable under complex, L-infinity perturbations of the coefficient matrix. Using a variant of the Tb Theorem, we also prove that the layer potentials are bounded and invertible on L-2(R-n) whenever A (x) is real and symmetric (and thus, by our stability result, also when A is complex, parallel to A - A(0)parallel to(infinity) is small enough and A(0) is real, symmetric, L-infinity and elliptic). In particular, we establish solvability of the Dirichlet and Neumann (and Regularity) problems, with L-2 (resp. (L) over dot(1)(2)) data, for small complex perturbations of a real symmetric matrix. Previously, L-2 solvability results for complex (or even real but non-symmetric) coefficients were known to hold only for perturbations of constant matrices (and then only for the Dirichlet problem), or in the special case that the coefficients A (j,n+1)= 0 = A(n+1,j), 1 andlt;= j andlt;= n, which corresponds to the Kato square root problem.
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| 9. |
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| 10. |
- Ameur, Yacin, et al.
(författare)
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Disk counting statistics near hard edges of random normal matrices: The multi-component regime
- 2024
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Ingår i: Advances in Mathematics. - : Elsevier BV. - 0001-8708 .- 1090-2082. ; 441
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Tidskriftsartikel (refereegranskat)abstract
- We consider a two-dimensional point process whose points are separated into two disjoint components by a hard wall, and study the multivariate moment generating function of the corresponding disk counting statistics. We investigate the “hard edge regime” where all disk boundaries are a distance of order [Formula presented] away from the hard wall, where n is the number of points. We prove that as n→+∞, the asymptotics of the moment generating function are of the form [Formula presented] and we determine the constants C1,…,C4 explicitly. The oscillatory term Fn is of order 1 and is given in terms of the Jacobi theta function. Our theorem allows us to derive various precise results on the disk counting function. For example, we prove that the asymptotic fluctuations of the number of points in one component are of order 1 and are given by an oscillatory discrete Gaussian. Furthermore, the variance of this random variable enjoys asymptotics described by the Weierstrass ℘-function.
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