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On Scaling Limits of Power Law Shot-noise Fields
Probability · Submitted 22 Apr 2014
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a $\alpha$-stable limit, intensity of the underlying point process goes to infinity.
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The abstract, sentence by sentence
This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a $\alpha$-stable limit, intensity of the underlying point process goes to infinity. It is also shown that the finite dimensional distributions of the limiting random field have i.i.d. stable random components. We hence propose to call this limte the $\alpha$- stable white noise field. Analogous results are also obtained for the extremal shot-noise field which converges to a Fr\'{e}chet white noise field. Finally, these results are applied to the analysis of wireless networks.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. | contribution 0.92 | 0.82 | 0.05 | asserted 0.91 |
| s1 | Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a $\alpha$-stable limit, intensity of the underlying point process goes to infinity. | result 0.99 | 0.91 | 0.65 | asserted 1.00 |
| s2 | It is also shown that the finite dimensional distributions of the limiting random field have i.i.d. stable random components. | result 1.00 | 0.92 | 0.16 | asserted 1.00 |
| s3 | We hence propose to call this limte the $\alpha$- stable white noise field. | interpretation 0.74 | 0.79 | 0.27 | asserted 0.57 |
| s4 | Analogous results are also obtained for the extremal shot-noise field which converges to a Fr\'{e}chet white noise field. | result 0.98 | 0.89 | 0.10 | asserted 1.00 |
| s5 | Finally, these results are applied to the analysis of wireless networks. | contribution 0.81 | 0.81 | 0.06 | asserted 0.99 |
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The paper
Original abstract
This article studies the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, it is shown that the shot-noise field can be scaled suitably to have a $\alpha$-stable limit, intensity of the underlying point process goes to infinity. It is also shown that the finite dimensional distributions of the limiting random field have i.i.d. stable random components. We hence propose to call this limte the $\alpha$- stable white noise field. Analogous results are also obtained for the extremal shot-noise field which converges to a Fr\'{e}chet white noise field. Finally, these results are applied to the analysis of wireless networks.
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