• Title, Summary, Keyword: ergodic theory

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EXAMPLES IN ERGODIC THEORY

  • Park, Kyewon Koh;Park, Seungseol
    • Korean Journal of Mathematics
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    • v.4 no.1
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    • pp.17-30
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    • 1996
  • In ergodic theory cutting and stacking constructions have been used to obtain a variety of important examples of transformations on the unit interval. We examine the example constructed by J. von Neumann and Kakutani and then apply the method used in the construction of Chacon's transformation to make examples that are weakly mixing but not mixing.

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Capacity Bounds on the Ergodic Capacity of Distributed MIMO Systems over K Fading Channels

  • Li, XingWang;Wang, Junfeng;Li, Lihua;Cavalcante, Charles C.
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.7
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    • pp.2992-3009
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    • 2016
  • The performance of D-MIMO systems is not only affected by multipath fading but also from shadowing fading, as well as path loss. In this paper, we investigate the ergodic capacity of D-MIMO systems operating in non-correlated K fading (Rayleigh/Gamma) channels. With the aid of majorization and Minkowski theory, we derive analytical closed-form expressions of the upper and lower bounds on the ergodic capacity for D-MIMO systems over non-correlated K fading channels, which are quite general and applicable for arbitrary signal-to-noise ratio (SNR) and the number of transceiver antennas. To intuitively reveal the impacts of system and fading parameters on the ergodic capacity, we deduce asymptotic approximations in the high and low SNR regimes. Finally, we pursue the massive MIMO systems analysis for the lower bound and derive closed-form expressions when the number of antennas at BS grows large, and when the number of antennas at transceivers becomes large with a fixed and finite ratio. It is demonstrated that the proposed expressions on the ergodic capacity accurately match with the theoretical analysis.

Applications of ergodic theory to pseudorandom numbers

  • Choe, Geon-Ho;Kim, Chihurn -Choe;Kim, Dong-Han -Choe
    • Bulletin of the Korean Mathematical Society
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    • v.35 no.1
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    • pp.173-187
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    • 1998
  • Several aspects of pseudorandom number generators are investigated from the viewpoint of ergodic theory. An algorithm of generating pseudorandom numbers proposed and shown to behave reasonably well.

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On Presentable Approximation for Nonlinear Noise

  • Kang, Jie-Hyung
    • Journal of the Chungcheong Mathematical Society
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    • v.5 no.1
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    • pp.23-34
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    • 1992
  • This is an extension of results of Wiener's nonlinear noise theory from noises generated by the Wiener process to noises generated by processes with stationary Gaussian increments. In particular, using Nisio's Approach, we show that every measurable ergodic noise can be approximated in law by Gaussian process-presentable noise.

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CONFORMAL DENSITY OF VISIBILITY MANIFOLD

  • Kim, Hyun-Jung
    • Bulletin of the Korean Mathematical Society
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    • v.38 no.1
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    • pp.211-222
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    • 2001
  • In this paper, we prove the existence and uniqueness of a $\delta(\Gamma)$-conformal density on the limit set of $\Gamma$ acting on visibility manifold H for a Fuchsian group $\Gamma$.

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Harmonics Analysis of Railroad Systems using Markov Chain (Markov Chain을 이용한 철도계통의 고조파 분석)

  • Song, Hak-Seon;Lee, Seung-Hyuk;Kim, Jin-O;Kim, Hyung-Chul
    • Proceedings of the KIEE Conference
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    • pp.230-233
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    • 2005
  • This paper proposes power qualify assessment using Markov Chain applied to Ergodic theorem. The Ergodic theorem introduces the state of aperiodic, recurrent, and non-null. The proposed method using Markov Chain presents very well generated harmonic characteristics according to the traction's operation of electric railway system. In case of infinite iteration, the characteristic of Markov Chain that converges on limiting probability Is able to expected harmonic currents posterior transient state. TDD(Total Demand Distortion) is also analyzed in expected current of each harmonic. The TDD for power quality assesment is calculated using Markov Chain theory in the Inceon international airport IAT power system.

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Performance Analysis Based on RAU Selection and Cooperation in Distributed Antenna Systems

  • Wang, Gang;Meng, Chao;Heng, Wei
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.12
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    • pp.5898-5916
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    • 2018
  • In this paper, the downlink performance of multi-cell distributed antenna systems (DAS) with a single user in each cell is investigated. Assuming the channel state information is available at the transmitter, four transmission modes are formulated as combinations of remote antenna units (RAUs) selection and cooperative transmission, namely, non-cooperative transmission without RAU selection (NCT), cooperative transmission without RAU selection (CT), non-cooperative transmission with RAU selection (NCT_RAUS), and cooperative transmission with RAU selection (CT_RAUS). By using probability theory, the cumulative distribution function (CDF) of a user's signal to interference plus noise ratio (SINR) and the system ergodic capacity under the above four modes are determined, and their closed-form expressions are obtained. Furthermore, the system energy efficiency (EE) is studied by introducing a realistic power consumption model of DAS. An expression for determining EE is formulated, and the closed-form tradeoff relationship between spectral efficiency (SE) and EE is derived as well. Simulation results demonstrate their consistency with the theoretical analysis and reveal the factors constraining system EE, which provide a scientific basis for future design and optimization of DAS.

Fault Tree Analysis and Reliability Analysis by Fuzzy Set Approach (퍼지집합에 의한 FT 분석 및 신뢰성분석)

  • Kim, Gil-Dong;Cho, Am
    • Journal of the Korean Society of Safety
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    • v.12 no.3
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    • pp.155-160
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    • 1997
  • The conventional fault tree and reliability analysis gives in many cases insufficient information concerning the relative frequencies of hazard events. This stems from that the basic events are not stationary and ergodic, and therefore the tolerances of the induced and top events cannot be calculated reliably based on the classical probability theory. To overcome this difficulty, the paper considers the relative frequencies of the basic events as fuzzy numbers and uses instead of probability, possible considerations for evaluating the mean values and tolerances of the top events. The possibility distribution of the basic events can be approximated based on heuristic considerations. This paper shows the use of these operators for constructing fault trees. The use of the method for numerical calculation is demonstrated on a field safety problem.

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CHARACTERIZATION OF TEMPERED EXPONENTIAL DICHOTOMIES

  • Barreira, Luis;Rijo, Joao;Valls, Claudia
    • Journal of the Korean Mathematical Society
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    • v.57 no.1
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    • pp.171-194
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    • 2020
  • For a nonautonomous dynamics defined by a sequence of bounded linear operators on a Banach space, we give a characterization of the existence of an exponential dichotomy with respect to a sequence of norms in terms of the invertibility of a certain linear operator between general admissible spaces. This notion of an exponential dichotomy contains as very special cases the notions of uniform, nonuniform and tempered exponential dichotomies. As applications, we detail the consequences of our results for the class of tempered exponential dichotomies, which are ubiquitous in the context of ergodic theory, and we show that the notion of an exponential dichotomy under sufficiently small parameterized perturbations persists and that their stable and unstable spaces are as regular as the perturbation.