By M. Aizenman (Chief Editor)

Articles during this volume:

1-21

Oseledets Regularity services for Anosov Flows

Slobodan N. Simić

23-57

Spectral size and Random Walks at the Dimensional Uniform Spanning Tree

Martin T. Barlow and Robert Masson

59-83

Ancient Dynamics in Bianchi types: method of Periodic Cycles

S. Liebscher, J. Härterich, okay. Webster and M. Georgi

85-97

Hastings’s Additivity Counterexample through Dvoretzky’s Theorem

Guillaume Aubrun, Stanisław Szarek and Elisabeth Werner

99-130

Deformations of Quantum box Theories on Spacetimes with Killing Vector Fields

Claudio Dappiaggi, Gandalf Lechner and Eric Morfa-Morales

131-151

The Vortex-Wave Equation with a unmarried Vortex because the restrict of the Euler Equation

Clayton Bjorland

153-198

On the structures of Holomorphic Vertex Operator Algebras of significant cost 24

Ching Hung Lam

199-220

Energy Cascades and Flux Locality in actual Scales of the 3D Navier-Stokes Equations

R. Dascaliuc and Z. Grujić

221-277

Spectral and Quantum Dynamical houses of the Weakly Coupled Fibonacci Hamiltonian

David Damanik and Anton Gorodetski

279-331

The Hamiltonian constitution of the Nonlinear Schrödinger Equation and the Asymptotic balance of its flooring States

Scipio Cuccagna

333-349

On the Self-Similar strategies of the 3D Euler and the comparable Equations

Dongho Chae

351-361

Weak-Strong area of expertise for Measure-Valued Solutions

Yann Brenier, Camillo De Lellis and László Székelyhidi

363-425

Effective Dynamics of Double Solitons for Perturbed mKdV

Justin Holmer, Galina Perelman and Maciej Zworski

427-440

Asymptotic Completeness in a category of Massless Relativistic Quantum box Theories

Wojciech Dybalski and Yoh Tanimoto

441-468

Symplectic Geometry of Entanglement

Adam Sawicki, Alan Huckleberry and Marek Kuś

469-485

An Algebraic model of Haag’s Theorem

Mihály Weiner

487-512

Unique Continuation for Schrödinger Evolutions, with purposes to Profiles of focus and touring Waves

L. Escauriaza, C. E. Kenig, G. Ponce and L. Vega

513-532

Constructing Self-Dual Strings

Christian Sämann

533-553

Hypercontractivity at the q-Araki-Woods Algebras

Hun Hee Lee and Éric Ricard

555-562

Second Eigenvalue of Paneitz Operators and suggest Curvature

Daguang Chen and Haizhong Li

563-604

On the preliminary stipulations and ideas of the Semiclassical Einstein Equations in a Cosmological Scenario

Nicola Pinamonti

605-631

Ornstein-Zernike Asymptotics for a common “Two-Particle” Lattice Operator

C. Boldrighini, R. A. Minlos and A. Pellegrinotti

633-639

Landau-Zener Tunneling for Dephasing Lindblad Evolutions

J. E. Avron, M. Fraas, G. M. Graf and P. Grech

641-656

The Dirac Operator on Generalized Taub-NUT Spaces

Andrei Moroianu and Sergiu Moroianu

657-710

Ground country at excessive Density

András Sütő

711-739

Scaling Limits of Random Skew aircraft walls with Arbitrarily Sloped again Walls

Sevak Mkrtchyan

741-796

Branching of Cantor Manifolds of Elliptic Tori and purposes to PDEs

Massimiliano Berti and Luca Biasco

797-826

‘Return to Equilibrium’ for Weakly Coupled Quantum structures: an easy Polymer Expansion

W. De Roeck and A. Kupiainen

827-843

A Generalized Grothendieck Inequality and Nonlocal Correlations that Require excessive Entanglement

Jop Briët, Harry Buhrman and Ben Toner

845

Erratum to: A KAM Theorem with purposes to Partial Differential Equations of upper Dimensions

Xiaoping Yuan

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**Extra resources for Communications in Mathematical Physics - Volume 305**

**Example text**

14), and using the bound |Dk | ≤ cδk−2 , we have −1/3 P G c ≤ Cδ0−2 22k exp(−cδ0−1 2k k −2 ) + exp(−c2k/3 δ0 ) k −1/3 ≤ Cδ0−2 e−cδ0 −1/3 ≤ Ce−c δ0 . 1 with ε = 1 4 gives λk G(δk−1r ) ≤ λk δ0 2−(k−1) G(δ0 r ) = 2λ0 δ0 2−k/2 G(δ0 r ). 1/2 1/2 1/2 1/2 So ∞ 1/2 1/2 1/2 λk G(δk−1r ) ≤ 5λ0 δ0 G(δ0 r ) = G(δ0 r ). k=1 Since B(0, r/2) ⊂ k Ak , we have B(0, r/2) ⊂ k Uk . Therefore on the event G, for 1/2 any x ∈ B(0, r/2), d(x, U0 ) ≤ G(δ0 r ). Further, on G, for each z ∈ Dk , we have γ (z, Uk−1 ) ⊂ Ak−1 .

8) is less than 1/4. Fix a further constant θ < 1, to be chosen later but which will depend only on δ0 . We begin the construction of U with an infinite LERW S started at 0 which gives the path γ0 = U0 = γ (0, ∞). Let z j , j = 1, . . σr ] chosen such that B j = B(z j , r/k) are disjoint. ) Let F1 = { S[σ2r , ∞) hits more than k/2 of B1 , . . Bk }, 1 F2 = {| S[0, σ2r ]| ≥ k 1/2 G(r )}. 20) −ck 1/2 . 7 below. If either F1 or F2 occurs, we terminate the algorithm with a ‘Type 1’ or ‘Type 2’ failure.

12, and let p > 0 be such that Ci (λ) ≤ Cλ p , i = 9, 10 and c11 (λ) ≥ cλ− p . We have ∞ E ω0 d(0, X T )q ≤ R q + E ω0 ≤ Rq + R 1(ek−1 R≤d(0,X T )

### Communications in Mathematical Physics - Volume 305 by M. Aizenman (Chief Editor)

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4.5