%PDF-1.5 % 4 0 obj << /S /GoTo /D (section.1) >> endobj 7 0 obj (Introduction) endobj 8 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 11 0 obj (Summary of results) endobj 12 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 15 0 obj (Notational conventions) endobj 16 0 obj << /S /GoTo /D (section.2) >> endobj 19 0 obj (Model description) endobj 20 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 23 0 obj (Definitions and connection to random walks) endobj 24 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 27 0 obj (Networks without disorder) endobj 28 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 31 0 obj (Average power and feasibility) endobj 32 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 35 0 obj (Random networks: disorder and erasures) endobj 36 0 obj << /S /GoTo /D (subsubsection.2.4.1) >> endobj 39 0 obj (The Anderson model) endobj 40 0 obj << /S /GoTo /D (subsubsection.2.4.2) >> endobj 43 0 obj (The erasure channel model) endobj 44 0 obj << /S /GoTo /D (section.3) >> endobj 47 0 obj (The Wyner model: Exact results) endobj 48 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 51 0 obj (Eigenvalue distribution) endobj 52 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 55 0 obj (The optimal power vector) endobj 56 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 59 0 obj (Feasibility analysis and probability of instability) endobj 60 0 obj << /S /GoTo /D (subsection.3.4) >> endobj 63 0 obj (Power distribution in the Wyner model) endobj 64 0 obj << /S /GoTo /D (subsection.3.5) >> endobj 67 0 obj (Bird's eye view of the Wyner model) endobj 68 0 obj << /S /GoTo /D (section.4) >> endobj 71 0 obj (Average power via the coherent potential approximation) endobj 72 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 75 0 obj (Numerical analysis and validation) endobj 76 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 79 0 obj (The breakdown of the CPA approach) endobj 80 0 obj << /S /GoTo /D (section.5) >> endobj 83 0 obj (Stability analysis) endobj 84 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 87 0 obj (Feasibility and instability in infinite networks) endobj 88 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 91 0 obj (Instability probability in finite networks: Lifshitz tails) endobj 92 0 obj << /S /GoTo /D (subsection.5.3) >> endobj 95 0 obj (Numerical validation in finite networks) endobj 96 0 obj << /S /GoTo /D (section.6) >> endobj 99 0 obj (Tails of the power distribution) endobj 100 0 obj << /S /GoTo /D (subsection.6.1) >> endobj 103 0 obj (A lower bound for the tails of the power distribution) endobj 104 0 obj << /S /GoTo /D (subsection.6.2) >> endobj 107 0 obj (An upper bound for nearest neighbor interactions) endobj 108 0 obj << /S /GoTo /D (section.7) >> endobj 111 0 obj (Long-term behavior of the power control dynamics) endobj 112 0 obj << /S /GoTo /D (section.8) >> endobj 115 0 obj (Conclusions) endobj 116 0 obj << /S /GoTo /D (section*.5) >> endobj 119 0 obj (Appendix A: Derivation of the CPA equations) endobj 120 0 obj << /S /GoTo /D (section*.6) >> endobj 123 0 obj (Appendix B: Derivation of the integrated density of states) endobj 124 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.1) >> endobj 127 0 obj (Approximation of N\(\) by NV\(\)) endobj 128 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.2) >> endobj 131 0 obj (Exchanging the order of the limits L and V) endobj 132 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.3) >> endobj 135 0 obj (The Laplace transform of NV) endobj 136 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.4) >> endobj 139 0 obj (An upper bound for N"0365N\(t\)) endobj 140 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.5) >> endobj 143 0 obj (A Lower Bound for N"0365N\(t\)) endobj 144 0 obj << /S /GoTo /D (subsubsection.Appendix.B.0.6) >> endobj 147 0 obj (Harvesting N\(\) from N"0365N\(t\)) endobj 148 0 obj << /S /GoTo /D (section*.7) >> endobj 151 0 obj (Appendix C: Continuous Approximation of H0) endobj 152 0 obj << /S /GoTo /D (section*.8) >> endobj 155 0 obj (Appendix D: Details for the bounds of the power distribution) endobj 156 0 obj << /S /GoTo /D (subsection.Appendix.D.1) >> endobj 159 0 obj (A lower bound for the distribution of power in the network) endobj 160 0 obj << /S /GoTo /D (subsection.Appendix.D.2) >> endobj 163 0 obj (A percolation-based upper bound) endobj 164 0 obj << /S /GoTo /D [165 0 R /FitH] >> endobj 175 0 obj << /Length 4362 /Filter /FlateDecode >> stream xڥ]s~/YO>t^};ٝLWK26%jO{ $A P*_UgWyPatte*O6"QIPFaci" "c߶q`moσ=_`ۆ1V~fߞݵԦpv{LaAXP¥cakvVv^7ҍns;8oL7ֹVpbc[kA]v(ʠ̀1`(REPDVA h_<6CFp@ISlIqSn>d3'dfۙX