Probability Theory

Klenke, Achim

doi:10.1007/978-1-84800-048-3

Cited by 143 publications

(91 citation statements)

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“…The uniform bounds proven above allow us to take the partial derivative with respect to η y outside the conditional average [21], and the resulting expression can then be integrated to prove Property 4.…”

Section: Finite Temperaturementioning

confidence: 99%

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Aizenman

Greenblatt

Lebowitz

2012

Journal of Mathematical Physics

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We prove that for quantum lattice systems in d ≤ 2 dimensions the addition of quenched disorder rounds any first order phase transition in the corresponding conjugate order parameter, both at positive temperatures and at T = 0. For systems with continuous symmetry the statement extends up to d ≤ 4 dimensions. This establishes for quantum systems the existence of the Imry-Ma phenomenon which for classical systems was proven by Aizenman and Wehr. The extension of the proof to quantum systems is achieved by carrying out the analysis at the level of thermodynamic quantities rather than equilibrium states.

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Section: Finite Temperaturementioning

confidence: 99%

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Aizenman

Greenblatt

Lebowitz

2012

Journal of Mathematical Physics

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“…3.1, in the IEEE 802.11 DCF, the transmission probability of a node is small, i.e., s i ( 1. In this case, the binomial distribution can be approximated to a Poisson distribution [19]. Moreover, the larger the number of the nodes in the network is, the more accurate the approximation is.…”

Section: Normalized Throughputmentioning

confidence: 99%

“…(7) and (12), it would be difficult to exactly derive the normalized throughput from Eqs. (17)- (19). Considering this problem, we use an approximate method to derive the normalized throughput of the network.…”

Section: Normalized Throughputmentioning

confidence: 99%

Performance modeling and analysis of IEEE 802.11 DCF based fair channel access for vehicle-to-roadside communication in a non-saturated state

Zheng

2014

Wireless Netw

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This paper considers the fair access problem in vehicular ad hoc networks and develops analytical models for analyzing the performance of an IEEE 802.11 distributed coordination function based fair channel access protocol in a non-saturated state. We first derive the relationship between the transmission probability and the minimum contention window size of a vehicle, and the relationship between the velocity and the minimum contention window size of a vehicle in a non-saturated state. Based on the analytical model, the minimum contention window size of a vehicle for a given velocity can be determined in order to achieve fair access among different vehicles. Moreover, an analytical model is also developed for analyzing the throughput performance of the fair channel access protocol in a non-saturated state. The effectiveness of the analytical models is justified through simulation results.

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“…Moreover, it is a Radon probability measure concentrated on U π [24,Theorem 4.1]. By the known portmanteau theorem [13,Theorem 13.16] and Fubini's theorem the invariance of Haar measures χ m together with (7) yield the following invariance properties under the right action…”

Section: Hardy Space Over U (∞)mentioning

confidence: 99%

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Lopushansky

2017

Results Math

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Abstract. An analog of the Paley-Wiener isomorphism for the Hardy space with an invariant measure over infinite-dimensional unitary groups is described. This allows us to investigate on such space the shift and multiplicative groups, as well as, their generators and intertwining operators. We show applications to the Gauss-Weierstrass semigroups and to the Weyl-Schrödinger irreducible representations of complexified infinitedimensional Heisenberg groups.Mathematics Subject Classification. 46T12, 46G20.

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Probability Theory

Cited by 143 publications

References 0 publications

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Proof of rounding by quenched disorder of first order transitions in low-dimensional quantum systems

Performance modeling and analysis of IEEE 802.11 DCF based fair channel access for vehicle-to-roadside communication in a non-saturated state

Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

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