Zobrazeno 1 - 10
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pro vyhledávání: '"Kozdron, Michael J."'
Autor:
Johnson, Kyler S., Kozdron, Michael J.
It is well-known in quantum information theory that a positive operator valued measure (POVM) is the most general kind of quantum measurement. Mathematically, a quantum probability is a normalised POVM, namely a function on certain subsets of a (loca
Externí odkaz:
http://arxiv.org/abs/1504.03829
We study essentially bounded quantum random variables and show that the Gelfand spectrum of such a quantum random variable coincides with the hypoconvex hull of its essential range. Moreover, a notion of operator-valued variance is introduced, leadin
Externí odkaz:
http://arxiv.org/abs/1502.03213
Kirchhoff's matrix tree theorem is a well-known result that gives a formula for the number of spanning trees in a finite, connected graph in terms of the graph Laplacian matrix. A closely related result is Wilson's algorithm for putting the uniform d
Externí odkaz:
http://arxiv.org/abs/1306.2059
Publikováno v:
J. Statist. Phys., volume 153, issue 1, pages 119-141, 2013
We outline a strategy for showing convergence of loop-erased random walk on the Z^2 square lattice to SLE(2), in the supremum norm topology that takes the time parametrization of the curves into account. The discrete curves are parametrized so that t
Externí odkaz:
http://arxiv.org/abs/1304.5013
Publikováno v:
J. Phys. A: Math. Theor., volume 45, number 49, paper 494015, 2012
We prove the existence of the Green's function for radial SLE(k) for k<8. Unlike the chordal case where an explicit formula for the Green's function is known for all values of k<8, we give an explicit formula only for k=4. For other values of k, we g
Externí odkaz:
http://arxiv.org/abs/1207.3721
Autor:
Farenick, Douglas, Kozdron, Michael J.
Publikováno v:
J. Math. Phys., volume 53, issue 4, paper 042201, 2012
A quantum probability measure is a function on a sigma-algebra of subsets of a (locally compact and Hausdorff) sample space that satisfies the formal requirements for a measure, but whose values are positive operators acting on a complex Hilbert spac
Externí odkaz:
http://arxiv.org/abs/1111.5638
Publikováno v:
Comm. Math. Phys., volume 318, issue 2, pages 307-354, 2013
We derive a rate of convergence of the Loewner driving function for planar loop-erased random walk to Brownian motion with speed 2 on the unit circle, the Loewner driving function for radial SLE(2). The proof uses a new estimate of the difference bet
Externí odkaz:
http://arxiv.org/abs/0911.3988
Autor:
Kozdron, Michael J.
Publikováno v:
J. Phys. A: Math. Theor., volume 42, number 26, paper 265003, 2009
We present a mathematical proof of theoretical predictions made by Arguin and Saint-Aubin, as well as by Bauer, Bernard, and Kytola, about certain non-local observables for the two-dimensional Ising model at criticality by combining Smirnov's recent
Externí odkaz:
http://arxiv.org/abs/0905.2430
Autor:
Alberts, Tom, Kozdron, Michael J.
Publikováno v:
Electron. Comm. Probab., volume 13, paper 43, pages 448-460, 2008
We derive a number of estimates for the probability that a chordal SLE path in the upper half plane H intersects a semicircle centred on the real line. We prove that if 0
Externí odkaz:
http://arxiv.org/abs/0707.3163
Autor:
Kozdron, Michael J.
Publikováno v:
C. R. Math. Rep. Acad. Sci. Canada, volume 29, number 3, pages 65-80, 2007
We review some recently completed research that establishes the scaling limit of Fomin's identity for loop-erased random walk on Z^2 in terms of the chordal Schramm-Loewner evolution (SLE) with parameter 2. In the case of two paths, we provide a simp
Externí odkaz:
http://arxiv.org/abs/math/0703615