论文标题
大偏差，Sharron-Mcmillan-Breiman定理用于超临界电信网络
Large Deviations, Sharron-McMillan-Breiman Theorem for Super-Critical Telecommunication Networks
论文作者
论文摘要
在本文中，我们获得了以信号交流比率网络为模型的超临界通信网络的大偏差渐近学。为此，我们定义了经验功率度量和经验连接度度量，并证明了两个不同尺度上的经验措施的联合大偏差原理（LDP），即$λ$和$λ$和$λ^2a_λ$ $λ$，其中$λ$是Poisson Pointing toperion for sinr forther the sinr forther的强度。以SINR网络为模型的随机电信网络。此外，我们证明了SINR网络的局部大偏差原理（LLDP）。从LLDP中，我们证明了一个大偏差原理，以及随机SNIR网络过程的经典Macmillian定理。注意，对于Tupical经验连接度量，$qπ\otimesπ，$我们可以从lldp a限制在sinr网络空间的基数上，大约等于$ \ displayStyle e^{λ^2 a_λ\ |qπ\otimesπ\ | h \ big（qπ\otimesπ/\ |qπ\otimesπ\ | \ big）}，其中$ q^{z^λ}的连接概率，$ q^{z^λ}，$满足$a_λ^{ - 1} q^{ - 1} q^{ - 1} q^{z^ld = qus，随机SINR网络的度量是在配备$τ-$拓扑的度量空间上获得的，并且在SINR网络过程的空间中获得了LLDP，而没有任何拓扑限制。
In this article we obtain large deviation asymptotics for supercritical communication networks modelled as signal-interference-noise ratio networks. To do this, we define the empirical power measure and the empirical connectivity measure, and prove joint large deviation principles(LDPs) for the two empirical measures on two different scales i.e. $λ$ and $λ^2 a_λ,$ where $λ$ is the intensity measure of the poisson point process (PPP) which defines the SINR random network.Using this joint LDPs we prove an asymptotic equipartition property for the stochastic telecommunication Networks modelled as the SINR networks. Further, we prove a Local large deviation principle(LLDP) for the SINR Network. From the LLDP we prove the a large deviation principle, and a classical MacMillian Theorem for the stochastic SNIR network processes. Note, for tupical empirical connectivity measure, $qπ\otimesπ,$ we can deduce from the LLDP a bound on the cardinality of the space of SINR networks to be approximately equal to $\displaystyle e^{λ^2 a_λ\|qπ\otimesπ\|H\big(qπ\otimesπ/\|qπ\otimesπ\|\big)},$ where the connectivity probability of the network, $Q^{z^λ} ,$ satisfies $ a_λ^{-1}Q^{z^λ} \to q.$ Observe, the LDP for the empirical measures of the stochastic SINR network were obtained on spaces of measures equipped with the $τ-$ topology, and the LLDPs were obtained in the space of SINR network process without any topological restrictions.
