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Volumn 19, Issue , 2014, Pages

Extinction probability and total progeny of predator-prey dynamics on infinite trees

Author keywords

Branching processes; Predator prey dynamics; SIR models

Indexed keywords


EID: 84893624744     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v19-2361     Document Type: Article
Times cited : (18)

References (24)
  • 1
    • 80052855975 scopus 로고    scopus 로고
    • Total progeny in killed branching random walk
    • MR-2834719
    • Luigi Addario-Berry and Nicolas Broutin, Total progeny in killed branching random walk, Probab. Theory Related Fields 151 (2011), no. 1-2, 265-295. MR-2834719
    • (2011) Probab. Theory Related Fields , vol.151 , Issue.1-2 , pp. 265-295
    • Addario-Berry, L.1    Broutin, N.2
  • 2
    • 78650428437 scopus 로고    scopus 로고
    • Tail asymptotics for the total progeny of the critical killed branching random walk
    • MR-2737710
    • Elie Aïdékon, Tail asymptotics for the total progeny of the critical killed branching random walk, Electron. Commun. Probab. 15 (2010), 522-533. MR-2737710
    • (2010) Electron. Commun. Probab. , vol.15 , pp. 522-533
    • Aïdékon, E.1
  • 4
    • 44949290839 scopus 로고
    • The "birth-and-assassination" process
    • MR-1078244
    • David Aldous and William Krebs, The "birth-and-assassination" process, Statist. Probab. Lett. 10 (1990), no. 5, 427-430. MR-1078244
    • (1990) Statist. Probab. Lett. , vol.10 , Issue.5 , pp. 427-430
    • Aldous, D.1    Krebs, W.2
  • 5
    • 0001373770 scopus 로고    scopus 로고
    • Epidemic models and social networks
    • MR-1746332
    • Håkan Andersson, Epidemic models and social networks, Math. Sci. 24 (1999), no. 2, 128-147. MR-1746332
    • (1999) Math. Sci. , vol.24 , Issue.2 , pp. 128-147
    • Andersson, H.1
  • 6
    • 84871003391 scopus 로고    scopus 로고
    • Dover Publications Inc., Mineola, NY, Reprint of the 1972 original [Springer, New York; MR0373040]. MR-0373040
    • Krishna B. Athreya and Peter E. Ney, Branching processes, Dover Publications Inc., Mineola, NY, 2004, Reprint of the 1972 original [Springer, New York; MR0373040]. MR-0373040
    • (2004) Branching processes
    • Athreya, K.B.1    Ney, P.E.2
  • 7
    • 79952837708 scopus 로고    scopus 로고
    • Survival probability of the branching random walk killed below a linear boundary
    • MR-2774095
    • Jean Bérard and Jean-Baptiste Gouéré, Survival probability of the branching random walk killed below a linear boundary, Electron. J. Probab. 16 (2011), no. 14, 396-418. MR-2774095
    • (2011) Electron. J. Probab. , vol.16 , Issue.14 , pp. 396-418
    • Bérard, J.1    Gouéré, J.-B.2
  • 8
    • 56549113106 scopus 로고    scopus 로고
    • On the birth-and-assassination process, with an application to scotching a rumor in a network
    • MR-2453554
    • Charles Bordenave, On the birth-and-assassination process, with an application to scotching a rumor in a network, Electron. J. Probab. 13 (2008), no. 66, 2014-2030. MR-2453554
    • (2008) Electron. J. Probab. , vol.13 , Issue.66 , pp. 2014-2030
    • Bordenave, C.1
  • 9
    • 0001425072 scopus 로고    scopus 로고
    • Shift in the velocity of a front due to a cutoff
    • MR-1473413
    • Eric Brunet and Bernard Derrida, Shift in the velocity of a front due to a cutoff, Phys. Rev. E (3) 56 (1997), no. 3, part A, 2597-2604. MR-1473413
    • (1997) Phys. Rev. E (3) , vol.56 , Issue.3 PART A , pp. 2597-2604
    • Brunet, E.1    Derrida, B.2
  • 10
    • 84870982275 scopus 로고    scopus 로고
    • Large deviations techniques and applications
    • Springer-Verlag, Berlin, Corrected reprint of the second (1998) edition. MR-2571413
    • Amir Dembo and Ofer Zeitouni, Large deviations techniques and applications, Stochastic Modelling and Applied Probability, vol. 38, Springer-Verlag, Berlin, 2010, Corrected reprint of the second (1998) edition. MR-2571413
    • (2010) Stochastic Modelling and Applied Probability , vol.38
    • Dembo, A.1    Zeitouni, O.2
  • 11
    • 79251491671 scopus 로고    scopus 로고
    • Asymptotics for the survival probability in a killed branching random walk
    • MR-2779399
    • Nina Gantert, Yueyun Hu, and Zhan Shi, Asymptotics for the survival probability in a killed branching random walk, Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011), no. 1, 111-129. MR-2779399
    • (2011) Ann. Inst. Henri Poincaré Probab. Stat. , vol.47 , Issue.1 , pp. 111-129
    • Gantert, N.1    Hu, Y.2    Shi, Z.3
  • 12
    • 0040042058 scopus 로고    scopus 로고
    • First passage percolation and a model for competing spatial growth
    • MR-1659548
    • Olle Häggström and Robin Pemantle, First passage percolation and a model for competing spatial growth, J. Appl. Probab. 35 (1998), no. 3, 683-692. MR-1659548
    • (1998) J. Appl. Probab. , vol.35 , Issue.3 , pp. 683-692
    • Häggström, O.1    Pemantle, R.2
  • 14
    • 0001128022 scopus 로고
    • Extension of a result of Seneta for the super-critical Galton-Watson process
    • MR-0254929
    • Christopher Heyde, Extension of a result of Seneta for the super-critical Galton-Watson process, Ann. Math. Statist. 41 (1970), 739-742. MR-0254929
    • (1970) Ann. Math. Statist. , vol.41 , pp. 739-742
    • Heyde, C.1
  • 15
    • 21244437645 scopus 로고    scopus 로고
    • The escape model on a homogeneous tree
    • (electronic). MR-2150700
    • George Kordzakhia, The escape model on a homogeneous tree, Electron. Comm. Probab. 10 (2005), 113-124 (electronic). MR-2150700
    • (2005) Electron. Comm. Probab. , vol.10 , pp. 113-124
    • Kordzakhia, G.1
  • 16
    • 16244369119 scopus 로고    scopus 로고
    • A two-species competition model on Zd
    • MR-2132598
    • George Kordzakhia and Steven P. Lalley, A two-species competition model on Zd, Stochastic Process. Appl. 115 (2005), no. 5, 781-796. MR-2132598
    • (2005) Stochastic Process. Appl. , vol.115 , Issue.5 , pp. 781-796
    • Kordzakhia, G.1    Lalley, S.P.2
  • 18
    • 79955048916 scopus 로고    scopus 로고
    • Effect of noise on front propagation in reaction-diffusion equations of KPP type
    • MR-2793860
    • Carl Mueller, Leonid Mytnik, and Jeremy Quastel, Effect of noise on front propagation in reaction-diffusion equations of KPP type, Invent. Math. 184 (2011), no. 2, 405-453. MR-2793860
    • (2011) Invent. Math. , vol.184 , Issue.2 , pp. 405-453
    • Mueller, C.1    Mytnik, L.2    Quastel, J.3
  • 19
    • 84884073625 scopus 로고    scopus 로고
    • (eds.), Princeton Studies in Complexity, Princeton University Press, Princeton, NJ, MR-2352222
    • Mark Newman, Albert-László Barabási, and Duncan J. Watts (eds.), The structure and dynamics of networks, Princeton Studies in Complexity, Princeton University Press, Princeton, NJ, 2006. MR-2352222
    • (2006) The structure and dynamics of networks
    • Newman, M.1    Barabási, A.-L.2    Watts, D.J.3
  • 20
    • 34547563505 scopus 로고    scopus 로고
    • Special issue on dynamic information dissemination
    • (Editors)
    • K. Ramamritham and P. Shenoy (Editors), Special issue on dynamic information dissemination, IEEE Internet Computing 11 (2007), 14-44.
    • (2007) IEEE Internet Computing , vol.11 , pp. 14-44
    • Ramamritham, K.1    Shenoy, P.2
  • 21
    • 84971848028 scopus 로고
    • Random growth in a tessellation
    • MR-0329079
    • Daniel Richardson, Random growth in a tessellation, Proc. Cambridge Philos. Soc. 74 (1973), 515-528. MR-0329079
    • (1973) Proc. Cambridge Philos. Soc. , vol.74 , pp. 515-528
    • Richardson, D.1
  • 22
    • 85048204775 scopus 로고    scopus 로고
    • In preparation. Available at Cambridge University Press, New York
    • Russell Lyons with Yuval Peres, Probability on trees and networks, In preparation. Available at http://mypage.iu.edu/~rdlyons/, Cambridge University Press, New York, 2007.
    • (2007) Probability on trees and networks
    • Lyons, R.1    Peres, Y.2
  • 23
    • 0002123491 scopus 로고
    • On recent theorems concerning the supercritical Galton-Watson process
    • MR-0234530
    • Eugene Seneta, On recent theorems concerning the supercritical Galton-Watson process., Ann. Math. Statist. 39 (1968), 2098-2102. MR-0234530
    • (1968) Ann. Math. Statist. , vol.39 , pp. 2098-2102
    • Seneta, E.1
  • 24
    • 0022752797 scopus 로고
    • The performance of a precedence-based queueing discipline
    • MR-0849031
    • John Tsitsiklis, Christos Papadimitriou, and Pierre Humblet, The performance of a precedence-based queueing discipline, J. Assoc. Comput. Mach. 33 (1986), no. 3, 593-602. MR-0849031
    • (1986) J. Assoc. Comput. Mach. , vol.33 , Issue.3 , pp. 593-602
    • Tsitsiklis, J.1    Papadimitriou, C.2    Humblet, P.3


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