Israel Journal of Mathematics
About: Israel Journal of Mathematics is an academic journal. The journal publishes majorly in the area(s): Banach space & Bounded function. It has an ISSN identifier of 0021-2172. Over the lifetime, 5725 publication(s) have been published receiving 122731 citation(s).
Papers published on a yearly basis
TL;DR: In this paper, the authors considered the limits of the uniform spanning tree and the loop-erased random walk (LERW) on a fine grid in the plane, as the mesh goes to zero.
Abstract: The uniform spanning tree (UST) and the loop-erased random walk (LERW) are strongly related probabilistic processes. We consider the limits of these models on a fine grid in the plane, as the mesh goes to zero. Although the existence of scaling limits is still unproven, subsequential scaling limits can be defined in various ways, and do exist. We establish some basic a.s. properties of these subsequential scaling limits in the plane. It is proved that any LERW subsequential scaling limit is a simple path, and that the trunk of any UST subsequential scaling limit is a topological tree, which is dense in the plane.
TL;DR: In this article, the maximum number of cliques possible in a graph with n nodes is determined and bounds are obtained for the number of different sizes of clique possible in such a graph.
Abstract: A clique is a maximal complete subgraph of a graph. The maximum number of cliques possible in a graph withn nodes is determined. Also, bounds are obtained for the number of different sizes of cliques possible in such a graph.
TL;DR: In this paper, the authors considered the setting of a map making "nice" return to a reference set, and defined criteria for the existence of equilibria, speed of convergence to equilibrium, and central limit theorem in terms of the tail of the return time function.
Abstract: The setting of this paper consists of a map making “nice” returns to a reference set. Criteria for the existence of equilibria, speed of convergence to equilibria and for the central limit theorem are given in terms of the tail of the return time function. The abstract setting considered arises naturally in differentiable dynamical systems with some expanding or hyperbolic properties.
TL;DR: In this paper, it was shown that any n point metric space is up to logn lipeomorphic to a subset of Hilbert space, and an example of ann point metric spaces which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn) is given.
Abstract: It is shown that anyn point metric space is up to logn lipeomorphic to a subset of Hilbert space. We also exhibit an example of ann point metric space which cannot be embedded in Hilbert space with distortion less than (logn)/(log logn), showing that the positive result is essentially best possible. The methods used are of probabilistic nature. For instance, to construct our example, we make use of random graphs.
TL;DR: In this paper, the authors extend Simon's theorem to a more general case, where the Schrodinger operator is essentially self-adjoint onC(R)m), if 0≦q ∈L>>\s 2(R>>\s m), andq>>\s 1(x)≧−q*(|x|) withq *(r) monotone nondecreasing inr ando(r petertodd 2) asr → ∞.
Abstract: Recently B. Simon proved a remarkable theorem to the effect that the Schrodinger operatorT=−Δ+q(x) is essentially selfadjoint onC 0 ∞ (R m if 0≦q ∈L 2(R m). Here we extend the theorem to a more general case,T=−Σ =1/ (∂/∂x j −ib j(x))2 +q 1(x) +q 2(x), whereb j, q1,q 2 are real-valued,b j ∈C(R m),q 1 ∈L loc 2 (R m),q 1(x)≧−q*(|x|) withq*(r) monotone nondecreasing inr ando(r 2) asr → ∞, andq 2 satisfies a mild Stummel-type condition. The point is that the assumption on the local behavior ofq 1 is the weakest possible. The proof, unlike Simon’s original one, is of local nature and depends on a distributional inequality and elliptic estimates.
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