Hirsch, Christian; Willhalm, Daniel Upper large deviations for power-weighted edge lengths in spatial random networks. (English) Zbl 07807055 Adv. Appl. Probab. 56, No. 1, 34-70 (2024). MSC: 60F10 60D05 60G55 05C99 PDFBibTeX XMLCite \textit{C. Hirsch} and \textit{D. Willhalm}, Adv. Appl. Probab. 56, No. 1, 34--70 (2024; Zbl 07807055) Full Text: DOI arXiv
Owada, Takashi; Yogeshwaran, D. Sub-tree counts on hyperbolic random geometric graphs. (English) Zbl 1503.60030 Adv. Appl. Probab. 54, No. 4, 1032-1069 (2022). MSC: 60F05 60D05 05C80 51M10 PDFBibTeX XMLCite \textit{T. Owada} and \textit{D. Yogeshwaran}, Adv. Appl. Probab. 54, No. 4, 1032--1069 (2022; Zbl 1503.60030) Full Text: DOI arXiv
Gracar, Peter; Lüchtrath, Lukas; Mörters, Peter Percolation phase transition in weight-dependent random connection models. (English) Zbl 1475.60198 Adv. Appl. Probab. 53, No. 4, 1090-1114 (2021). MSC: 60K35 05C80 PDFBibTeX XMLCite \textit{P. Gracar} et al., Adv. Appl. Probab. 53, No. 4, 1090--1114 (2021; Zbl 1475.60198) Full Text: DOI arXiv
Torrisi, Giovanni Luca; Leonardi, Emilio Almost sure central limit theorems in stochastic geometry. (English) Zbl 1473.60057 Adv. Appl. Probab. 52, No. 3, 705-734 (2020). MSC: 60F05 60G55 05C80 60D05 52C99 PDFBibTeX XMLCite \textit{G. L. Torrisi} and \textit{E. Leonardi}, Adv. Appl. Probab. 52, No. 3, 705--734 (2020; Zbl 1473.60057) Full Text: DOI arXiv
Müller, Tobias; Staps, Merlijn The diameter of KPKVB random graphs. (English) Zbl 1427.05212 Adv. Appl. Probab. 51, No. 2, 358-377 (2019). MSC: 05C80 05C82 05C12 60D05 82B43 PDFBibTeX XMLCite \textit{T. Müller} and \textit{M. Staps}, Adv. Appl. Probab. 51, No. 2, 358--377 (2019; Zbl 1427.05212) Full Text: DOI arXiv
van Lieshout, M. N. M. Nearest-neighbour Markov point processes on graphs with Euclidean edges. (English) Zbl 1443.60047 Adv. Appl. Probab. 50, No. 4, 1275-1293 (2018). MSC: 60G55 60D05 PDFBibTeX XMLCite \textit{M. N. M. van Lieshout}, Adv. Appl. Probab. 50, No. 4, 1275--1293 (2018; Zbl 1443.60047) Full Text: DOI arXiv
Chenavier, Nicolas; Devillers, Olivier Stretch factor in a planar Poisson-Delaunay triangulation with a large intensity. (English) Zbl 1431.60012 Adv. Appl. Probab. 50, No. 1, 35-56 (2018). MSC: 60D05 05C80 PDFBibTeX XMLCite \textit{N. Chenavier} and \textit{O. Devillers}, Adv. Appl. Probab. 50, No. 1, 35--56 (2018; Zbl 1431.60012) Full Text: DOI
Last, Günter; Ziesche, Sebastian On the Ornstein-Zernike equation for stationary cluster processes and the random connection model. (English) Zbl 1423.60159 Adv. Appl. Probab. 49, No. 4, 1260-1287 (2017). MSC: 60K35 60D05 60G55 PDFBibTeX XMLCite \textit{G. Last} and \textit{S. Ziesche}, Adv. Appl. Probab. 49, No. 4, 1260--1287 (2017; Zbl 1423.60159) Full Text: DOI arXiv
García Trillos, Nicolás; Slepčev, Dejan; von Brecht, James Estimating perimeter using graph cuts. (English) Zbl 1425.60014 Adv. Appl. Probab. 49, No. 4, 1067-1090 (2017). MSC: 60D05 62G20 68R10 PDFBibTeX XMLCite \textit{N. García Trillos} et al., Adv. Appl. Probab. 49, No. 4, 1067--1090 (2017; Zbl 1425.60014) Full Text: DOI arXiv
Li, Anshui; Müller, Tobias On the treewidth of random geometric graphs and percolated grids. (English) Zbl 1428.05284 Adv. Appl. Probab. 49, No. 1, 49-60 (2017). MSC: 05C80 60D05 82B43 PDFBibTeX XMLCite \textit{A. Li} and \textit{T. Müller}, Adv. Appl. Probab. 49, No. 1, 49--60 (2017; Zbl 1428.05284) Full Text: DOI
Díaz, J.; Mitsche, D.; Perarnau, G.; Pérez-Giménez, X. On the relation between graph distance and Euclidean distance in random geometric graphs. (English) Zbl 1348.05188 Adv. Appl. Probab. 48, No. 3, 848-864 (2016). MSC: 05C80 68R10 PDFBibTeX XMLCite \textit{J. Díaz} et al., Adv. Appl. Probab. 48, No. 3, 848--864 (2016; Zbl 1348.05188) Full Text: DOI arXiv Euclid Link
Xia, Aihua; Yukich, J. E. Normal approximation for statistics of Gibbsian input in geometric probability. (English) Zbl 1333.60037 Adv. Appl. Probab. 47, No. 4, 934-972 (2015). MSC: 60F05 60G55 60D05 05C80 91B30 PDFBibTeX XMLCite \textit{A. Xia} and \textit{J. E. Yukich}, Adv. Appl. Probab. 47, No. 4, 934--972 (2015; Zbl 1333.60037) Full Text: DOI arXiv Euclid
Jordan, Jonathan; Wade, Andrew R. Phase transitions for random geometric preferential attachment graphs. (English) Zbl 1364.60019 Adv. Appl. Probab. 47, No. 2, 565-588 (2015). MSC: 60D05 05C80 90B15 PDFBibTeX XMLCite \textit{J. Jordan} and \textit{A. R. Wade}, Adv. Appl. Probab. 47, No. 2, 565--588 (2015; Zbl 1364.60019) Full Text: DOI arXiv Euclid Link
Hirsch, C.; Neuhäuser, D.; Gloaguen, C.; Schmidt, V. First passage percolation on random geometric graphs and an application to shortest-path trees. (English) Zbl 1355.60018 Adv. Appl. Probab. 47, No. 2, 328-354 (2015). Reviewer: Alan A. Sola (Stockholm) MSC: 60D05 05C80 05C10 82B43 PDFBibTeX XMLCite \textit{C. Hirsch} et al., Adv. Appl. Probab. 47, No. 2, 328--354 (2015; Zbl 1355.60018) Full Text: DOI Euclid
Ganesan, Ghurumuruhan Infection spread in random geometric graphs. (English) Zbl 1337.60242 Adv. Appl. Probab. 47, No. 1, 164-181 (2015). MSC: 60K35 60J10 60C05 62E10 05C80 92D30 PDFBibTeX XMLCite \textit{G. Ganesan}, Adv. Appl. Probab. 47, No. 1, 164--181 (2015; Zbl 1337.60242) Full Text: DOI Euclid
Chen, Ge; Yao, Changlong; Guo, Tiande The asymptotic size of the largest component in random geometric graphs with some applications. (English) Zbl 1296.60259 Adv. Appl. Probab. 46, No. 2, 307-324 (2014). Reviewer: Guy Jumarie (Montréal) MSC: 60K35 60D05 82B43 PDFBibTeX XMLCite \textit{G. Chen} et al., Adv. Appl. Probab. 46, No. 2, 307--324 (2014; Zbl 1296.60259) Full Text: DOI arXiv Euclid
Hirsch, C.; Neuhäuser, D.; Schmidt, V. Connectivity of random geometric graphs related to minimal spanning forests. (English) Zbl 1268.60066 Adv. Appl. Probab. 45, No. 1, 20-36 (2013). Reviewer: Ove Frank (Stockholm) MSC: 60G55 05C10 60D05 05C80 82B43 PDFBibTeX XMLCite \textit{C. Hirsch} et al., Adv. Appl. Probab. 45, No. 1, 20--36 (2013; Zbl 1268.60066) Full Text: DOI Euclid
Falgas-Ravry, Victor; Walters, Mark Sharpness in the \(k\)-nearest-neighbours random geometric graph model. (English) Zbl 1278.60142 Adv. Appl. Probab. 44, No. 3, 617-634 (2012). MSC: 60K35 82B43 PDFBibTeX XMLCite \textit{V. Falgas-Ravry} and \textit{M. Walters}, Adv. Appl. Probab. 44, No. 3, 617--634 (2012; Zbl 1278.60142) Full Text: DOI arXiv Euclid
Iyer, Srikanth K.; Yogeshwaran, D. Percolation and connectivity in \(AB\) random geometric graphs. (English) Zbl 1248.60016 Adv. Appl. Probab. 44, No. 1, 21-41 (2012). Reviewer: Nikolaos Fountoulakis (Edgbaston) MSC: 60D05 05C80 05C40 60K35 PDFBibTeX XMLCite \textit{S. K. Iyer} and \textit{D. Yogeshwaran}, Adv. Appl. Probab. 44, No. 1, 21--41 (2012; Zbl 1248.60016) Full Text: DOI arXiv
Bonichon, Nicolas; Marckert, Jean-François Asymptotics of geometrical navigation on a random set of points in the plane. (English) Zbl 1238.60014 Adv. Appl. Probab. 43, No. 4, 899-942 (2011). Reviewer: Ilya S. Molchanov (Bern) MSC: 60D05 60B10 60G55 68W40 PDFBibTeX XMLCite \textit{N. Bonichon} and \textit{J.-F. Marckert}, Adv. Appl. Probab. 43, No. 4, 899--942 (2011; Zbl 1238.60014) Full Text: DOI arXiv
Baccelli, François; Błaszczyszyn, Bartłomiej; Haji-Mirsadeghi, Mir-Omid Optimal paths on the space-time SINR random graph. (English) Zbl 1223.60011 Adv. Appl. Probab. 43, No. 1, 131-150 (2011). Reviewer: Nikolaos Fountoulakis (Edgbaston) MSC: 60D05 05C80 90C27 60G55 PDFBibTeX XMLCite \textit{F. Baccelli} et al., Adv. Appl. Probab. 43, No. 1, 131--150 (2011; Zbl 1223.60011) Full Text: DOI arXiv
Voss, Florian; Gloaguen, Catherine; Schmidt, Volker Scaling limits for shortest path lengths along the edges of stationary tessellations. (English) Zbl 1214.60006 Adv. Appl. Probab. 42, No. 4, 936-952 (2010). Reviewer: Viktor Ohanyan (Erevan) MSC: 60D05 60G55 52C20 90B15 PDFBibTeX XMLCite \textit{F. Voss} et al., Adv. Appl. Probab. 42, No. 4, 936--952 (2010; Zbl 1214.60006) Full Text: DOI arXiv
Penrose, Mathew D.; Wade, Andrew R. Limit theorems for random spatial drainage networks. (English) Zbl 1208.60010 Adv. Appl. Probab. 42, No. 3, 659-688 (2010). Reviewer: Ove Frank (Stockholm) MSC: 60D05 60F05 90B15 60F25 05C80 PDFBibTeX XMLCite \textit{M. D. Penrose} and \textit{A. R. Wade}, Adv. Appl. Probab. 42, No. 3, 659--688 (2010; Zbl 1208.60010) Full Text: DOI arXiv
Gupta, Bhupender; Iyer, Srikanth K. Criticality of the exponential rate of decay for the largest nearest-neighbor link in random geometric graphs. (English) Zbl 1206.60014 Adv. Appl. Probab. 42, No. 3, 631-658 (2010). MSC: 60D05 60G70 05C05 90C27 PDFBibTeX XMLCite \textit{B. Gupta} and \textit{S. K. Iyer}, Adv. Appl. Probab. 42, No. 3, 631--658 (2010; Zbl 1206.60014) Full Text: DOI arXiv
Jordan, Jonathan Degree sequences of geometric preferential attachment graphs. (English) Zbl 1210.05158 Adv. Appl. Probab. 42, No. 2, 319-330 (2010). MSC: 05C80 60D05 PDFBibTeX XMLCite \textit{J. Jordan}, Adv. Appl. Probab. 42, No. 2, 319--330 (2010; Zbl 1210.05158) Full Text: DOI
Balister, Paul; Bollobás, Béla; Sarkar, Amites; Walters, Mark Sentry selection in wireless networks. (English) Zbl 1209.05221 Adv. Appl. Probab. 42, No. 1, 1-25 (2010). MSC: 05C80 60D05 82B43 PDFBibTeX XMLCite \textit{P. Balister} et al., Adv. Appl. Probab. 42, No. 1, 1--25 (2010; Zbl 1209.05221) Full Text: DOI
Devroye, Luc; Gudmundsson, Joachim; Morin, Pat On the expected maximum degree of Gabriel and Yao graphs. (English) Zbl 1196.60019 Adv. Appl. Probab. 41, No. 4, 1123-1140 (2009). MSC: 60D05 68U05 52C99 PDFBibTeX XMLCite \textit{L. Devroye} et al., Adv. Appl. Probab. 41, No. 4, 1123--1140 (2009; Zbl 1196.60019) Full Text: DOI
Díaz, J.; Mitsche, D.; Pérez-Giménez, X. On the probability of the existence of fixed-size components in random geometric graphs. (English) Zbl 1192.68478 Adv. Appl. Probab. 41, No. 2, 344-357 (2009). MSC: 68R10 60C05 PDFBibTeX XMLCite \textit{J. Díaz} et al., Adv. Appl. Probab. 41, No. 2, 344--357 (2009; Zbl 1192.68478) Full Text: DOI
Balister, Paul; Bollobás, Béla; Walters, Mark Random transceiver networks. (English) Zbl 1220.60056 Adv. Appl. Probab. 41, No. 2, 323-343 (2009). MSC: 60K35 82B43 90B18 PDFBibTeX XMLCite \textit{P. Balister} et al., Adv. Appl. Probab. 41, No. 2, 323--343 (2009; Zbl 1220.60056) Full Text: DOI
Balister, Paul; Bollobás, Béla; Sarkar, Amites; Walters, Mark A critical constant for the \(k\) nearest-neighbour model. (English) Zbl 1160.05333 Adv. Appl. Probab. 41, No. 1, 1-12 (2009). MSC: 05C80 05C40 60G55 82B43 PDFBibTeX XMLCite \textit{P. Balister} et al., Adv. Appl. Probab. 41, No. 1, 1--12 (2009; Zbl 1160.05333) Full Text: DOI arXiv
Hansen, Jennie C.; Schmutz, Eric; Sheng, Li Covering random points in a unit disk. (English) Zbl 1138.60011 Adv. Appl. Probab. 40, No. 1, 22-30 (2008). MSC: 60D05 68R10 PDFBibTeX XMLCite \textit{J. C. Hansen} et al., Adv. Appl. Probab. 40, No. 1, 22--30 (2008; Zbl 1138.60011) Full Text: DOI
Aldous, David J.; Kendall, Wilfrid S. Short-length routes in low-cost networks via Poisson line patterns. (English) Zbl 1167.60004 Adv. Appl. Probab. 40, No. 1, 1-21 (2008). Reviewer: Hans Daduna (Hamburg) MSC: 60D05 90B15 90B10 05C80 PDFBibTeX XMLCite \textit{D. J. Aldous} and \textit{W. S. Kendall}, Adv. Appl. Probab. 40, No. 1, 1--21 (2008; Zbl 1167.60004) Full Text: DOI arXiv
Wade, Andrew R. Explicit laws of large numbers for random nearest-neighbour-type graphs. (English) Zbl 1122.60012 Adv. Appl. Probab. 39, No. 2, 326-342 (2007). MSC: 60D05 60F25 PDFBibTeX XMLCite \textit{A. R. Wade}, Adv. Appl. Probab. 39, No. 2, 326--342 (2007; Zbl 1122.60012) Full Text: DOI arXiv Euclid
Bai, Z. D.; Lee, Sungchul; Penrose, Mathew D. Rooted edges of a minimal directed spanning tree on random points. (English) Zbl 1094.60004 Adv. Appl. Probab. 38, No. 1, 1-30 (2006). Reviewer: Wiesław Dziubdziela (Kielce) MSC: 60D05 60G70 05C80 60F05 PDFBibTeX XMLCite \textit{Z. D. Bai} et al., Adv. Appl. Probab. 38, No. 1, 1--30 (2006; Zbl 1094.60004) Full Text: DOI
Balister, Paul; Bollobás, Béla; Sarkar, Amites; Walters, Mark Connectivity of random \(k\)-nearest-neighbour graphs. (English) Zbl 1079.05086 Adv. Appl. Probab. 37, No. 1, 1-24 (2005). Reviewer: Ove Frank (Stockholm) MSC: 05C80 82B43 60G55 60F20 PDFBibTeX XMLCite \textit{P. Balister} et al., Adv. Appl. Probab. 37, No. 1, 1--24 (2005; Zbl 1079.05086) Full Text: DOI
Penrose, Mathew D.; Wade, Andrew R. Random minimal directed spanning trees and Dickman-type distributions. (English) Zbl 1068.60023 Adv. Appl. Probab. 36, No. 3, 691-714 (2004). Reviewer: Gregory Loren McColm (Tampa) MSC: 60D05 05C80 05D40 60F99 60G70 PDFBibTeX XMLCite \textit{M. D. Penrose} and \textit{A. R. Wade}, Adv. Appl. Probab. 36, No. 3, 691--714 (2004; Zbl 1068.60023) Full Text: DOI Link
Chiu, S. N.; Molchanov, I. S. A new graph related to the directions of nearest neighbours in a point process. (English) Zbl 1031.60040 Adv. Appl. Probab. 35, No. 1, 47-55 (2003). Reviewer: B.Grigelionis (Vilnius) MSC: 60G55 60D05 60F05 62H11 PDFBibTeX XMLCite \textit{S. N. Chiu} and \textit{I. S. Molchanov}, Adv. Appl. Probab. 35, No. 1, 47--55 (2003; Zbl 1031.60040) Full Text: DOI
Penrose, Mathew D. Focusing of the scan statistic and geometric clique number. (English) Zbl 1031.60046 Adv. Appl. Probab. 34, No. 4, 739-753 (2002). Reviewer: Ljuben Mutafchiev (Sofia) MSC: 60G70 60D05 05C80 PDFBibTeX XMLCite \textit{M. D. Penrose}, Adv. Appl. Probab. 34, No. 4, 739--753 (2002; Zbl 1031.60046) Full Text: DOI
Bertin, Etienne; Billiot, Jean-Michel; Drouilhet, Rémy Continuum percolation in the Gabriel graph. (English) Zbl 1020.60003 Adv. Appl. Probab. 34, No. 4, 689-701 (2002). MSC: 60D05 62B05 PDFBibTeX XMLCite \textit{E. Bertin} et al., Adv. Appl. Probab. 34, No. 4, 689--701 (2002; Zbl 1020.60003) Full Text: DOI
McGivney, K.; Yukich, J. E. Asymptotics for geometric location problems over random samples. (English) Zbl 0944.60024 Adv. Appl. Probab. 31, No. 3, 632-642 (1999). Reviewer: N.G.Gamkrelidze (Moskva) MSC: 60D05 60F15 05C80 90B80 PDFBibTeX XMLCite \textit{K. McGivney} and \textit{J. E. Yukich}, Adv. Appl. Probab. 31, No. 3, 632--642 (1999; Zbl 0944.60024) Full Text: DOI
Chin, Y. C.; Baddeley, A. J. On connected component Markov point processes. (English) Zbl 0953.60033 Adv. Appl. Probab. 31, No. 2, 279-282 (1999). Reviewer: B.P.Harlamov (St.Peterburg) MSC: 60G55 60D05 PDFBibTeX XMLCite \textit{Y. C. Chin} and \textit{A. J. Baddeley}, Adv. Appl. Probab. 31, No. 2, 279--282 (1999; Zbl 0953.60033) Full Text: DOI Link
Penrose, Mathew D. Extremes for the minimal spanning tree on normally distributed points. (English) Zbl 0919.60025 Adv. Appl. Probab. 30, No. 3, 628-639 (1998). MSC: 60D05 60G70 05C05 90C27 PDFBibTeX XMLCite \textit{M. D. Penrose}, Adv. Appl. Probab. 30, No. 3, 628--639 (1998; Zbl 0919.60025) Full Text: DOI
Appel, Martin J. B.; Russo, Ralph P. The minimum vertex degree of a graph on uniform points in \([0,1]^d\). (English) Zbl 0899.05061 Adv. Appl. Probab. 29, No. 3, 582-594 (1997). Reviewer: O.Frank (Stockholm) MSC: 05C80 60C05 60D05 PDFBibTeX XMLCite \textit{M. J. B. Appel} and \textit{R. P. Russo}, Adv. Appl. Probab. 29, No. 3, 582--594 (1997; Zbl 0899.05061) Full Text: DOI
Appel, Martin J. B.; Russo, Ralph P. The maximum vertex degree of a graph on uniform points in \([0,1]^d\). (English) Zbl 0899.05060 Adv. Appl. Probab. 29, No. 3, 567-581 (1997). Reviewer: O.Frank (Stockholm) MSC: 05C80 60C05 60D05 PDFBibTeX XMLCite \textit{M. J. B. Appel} and \textit{R. P. Russo}, Adv. Appl. Probab. 29, No. 3, 567--581 (1997; Zbl 0899.05060) Full Text: DOI
Barndorff-Nielsen, O. E. A note on electrical networks and the inverse Gaussian distribution. (English) Zbl 0792.60015 Adv. Appl. Probab. 26, No. 1, 63-67 (1994). MSC: 60E99 60B99 60K35 60D05 62E99 PDFBibTeX XMLCite \textit{O. E. Barndorff-Nielsen}, Adv. Appl. Probab. 26, No. 1, 63--67 (1994; Zbl 0792.60015) Full Text: DOI
Cowan, Richard; Tsang, Albert K. L. The falling-leaves mosaic and its equilibrium properties. (English) Zbl 0792.60012 Adv. Appl. Probab. 26, No. 1, 54-62 (1994). MSC: 60D05 05B45 05C80 52C15 PDFBibTeX XMLCite \textit{R. Cowan} and \textit{A. K. L. Tsang}, Adv. Appl. Probab. 26, No. 1, 54--62 (1994; Zbl 0792.60012) Full Text: DOI