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A central limit theorem for pulled fronts in a random medium
1. | Department of Mathematics, Duke University, Box 90320, Durham, NC, 27708-0320, United States |
References:
[1] |
M. Bages, P. Martinez and J.-M. Roquejoffre, How traveling waves attract the solutions of KPP-type equations,, preprint 2010., (2010). Google Scholar |
[2] |
H. Berestycki and F. Hamel, Front propagation in periodic excitable media,, Comm. Pure Appl. Math., 55 (2002), 949.
doi: 10.1002/cpa.3022. |
[3] |
H. Berestycki and F. Hamel, Generalized travelling waves for reaction-diffusion equations,, In:, 446 (2007), 101.
|
[4] |
P. Billingsley, "Convergence of Probability Measures,", John Wiley and Sons, (1968).
|
[5] |
E. Brunet, B. Derrida, A. H. Mueller and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts,, Phys. Rev. E, 73 (2006).
doi: 10.1103/PhysRevE.73.056126. |
[6] |
S. Chatterjee, A new method of normal approximation,, Ann. Probab., 36 (2008), 1584.
doi: 10.1214/07-AOP370. |
[7] |
R. Fisher, The wave of advance of advantageous genes,, Ann. Eugenics, 7 (1937), 355.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[8] |
M. Freidlin, "Functional Integration and Partial Differential Equations,", Ann. Math. Stud. 109, (1985).
|
[9] |
J. Gärtner and M. I. Freidlin, The propagation of concentration waves in periodic and random media,, Dokl. Acad. Nauk SSSR, 249 (1979), 521.
|
[10] |
P. Hall and C. C. Heyde, "Martingale Limit Theory and its Application,", Academic Press, (1980).
|
[11] |
F. Hamel and L. Roques, Uniqueness and stability properties of monostable pulsating fronts,, J. European Math. Soc., 13 (2011), 345.
doi: 10.4171/JEMS/256. |
[12] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, Étude de l'équation de la chaleurde matiére et son application à un problème biologique,, Bull. Moskov. Gos. Univ. Mat. Mekh., 1 (1937), 1. Google Scholar |
[13] |
P.-L. Lions and P. E. Souganidis, Homogenization of viscous Hamilton-Jacobi equations in stationary ergodic media,, Comm. Partial Diff. Eqn., 30 (2005), 335.
doi: 10.1081/PDE-200050077. |
[14] |
A. Majda and P. E. Souganidis, Flame fronts in a turbulent combustion model with fractal velocity fields,, Comm. Pure Appl. Math., 51 (1998), 1337.
doi: 10.1002/(SICI)1097-0312(199811/12)51:11/12<1337::AID-CPA4>3.0.CO;2-B. |
[15] |
P. Martinez and J.-M. Roquejoffre, Convergence to critical waves in KPP-type equations,, Preprint 2010., (2010). Google Scholar |
[16] |
A. Mellet, J. Nolen, J.-M. Roquejoffre and L. Ryzhik, Stability of generalized transition fronts,, Communications in PDE, 34 (2009), 521.
doi: 10.1080/03605300902768677. |
[17] |
C. Mueller and R. Sowers, Random travelling waves for the KPP equation with noise,, J. Funct. Anal., 128 (1995), 439.
doi: 10.1006/jfan.1995.1038. |
[18] |
J. Nolen, An invariance principle for random traveling waves in one dimension,, SIAM J. Math. Anal., 43 (2011), 153.
doi: 10.1137/090746513. |
[19] |
J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium,, AIHP - Analyse Non Linéaire, 26 (2009), 1021.
|
[20] |
J. Nolen and J. Xin, Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows,, AIHP - Analyse Non Linéaire, 26 (2008), 815.
|
[21] |
J. Nolen and J. Xin, KPP fronts in 1D random drift,, Discrete and Continuous Dynamical Systems B, 11 (2009), 421.
doi: 10.3934/dcdsb.2009.11.421. |
[22] |
A. Rocco, U. Ebert and W. van Saarloos, Subdiffusive fluctuations of "pulled" fronts with multiplicative noise,, Phys. Rev. E, 62 (2000).
doi: 10.1103/PhysRevE.62.R13. |
[23] |
W. Shen, Traveling waves in diffusive random media,, J. Dynamics and Diff. Eqns., 16 (2004), 1011.
doi: 10.1007/s10884-004-7832-x. |
[24] |
R. Tribe, A travelling wave solution to the Kolmogorov equation with noise,, Stochastics Stochastics Rep., 56 (1996), 317.
|
[25] |
W. van Saarloos, Front propagation into unstable states,, Physics Reports, 386 (2003), 29.
doi: 10.1016/j.physrep.2003.08.001. |
[26] |
J. Xin, "An Introduction to Fronts in Random Media,", Springer, (2009).
doi: 10.1007/978-0-387-87683-2. |
show all references
References:
[1] |
M. Bages, P. Martinez and J.-M. Roquejoffre, How traveling waves attract the solutions of KPP-type equations,, preprint 2010., (2010). Google Scholar |
[2] |
H. Berestycki and F. Hamel, Front propagation in periodic excitable media,, Comm. Pure Appl. Math., 55 (2002), 949.
doi: 10.1002/cpa.3022. |
[3] |
H. Berestycki and F. Hamel, Generalized travelling waves for reaction-diffusion equations,, In:, 446 (2007), 101.
|
[4] |
P. Billingsley, "Convergence of Probability Measures,", John Wiley and Sons, (1968).
|
[5] |
E. Brunet, B. Derrida, A. H. Mueller and S. Munier, Phenomenological theory giving the full statistics of the position of fluctuating pulled fronts,, Phys. Rev. E, 73 (2006).
doi: 10.1103/PhysRevE.73.056126. |
[6] |
S. Chatterjee, A new method of normal approximation,, Ann. Probab., 36 (2008), 1584.
doi: 10.1214/07-AOP370. |
[7] |
R. Fisher, The wave of advance of advantageous genes,, Ann. Eugenics, 7 (1937), 355.
doi: 10.1111/j.1469-1809.1937.tb02153.x. |
[8] |
M. Freidlin, "Functional Integration and Partial Differential Equations,", Ann. Math. Stud. 109, (1985).
|
[9] |
J. Gärtner and M. I. Freidlin, The propagation of concentration waves in periodic and random media,, Dokl. Acad. Nauk SSSR, 249 (1979), 521.
|
[10] |
P. Hall and C. C. Heyde, "Martingale Limit Theory and its Application,", Academic Press, (1980).
|
[11] |
F. Hamel and L. Roques, Uniqueness and stability properties of monostable pulsating fronts,, J. European Math. Soc., 13 (2011), 345.
doi: 10.4171/JEMS/256. |
[12] |
A. N. Kolmogorov, I. G. Petrovskii and N. S. Piskunov, Étude de l'équation de la chaleurde matiére et son application à un problème biologique,, Bull. Moskov. Gos. Univ. Mat. Mekh., 1 (1937), 1. Google Scholar |
[13] |
P.-L. Lions and P. E. Souganidis, Homogenization of viscous Hamilton-Jacobi equations in stationary ergodic media,, Comm. Partial Diff. Eqn., 30 (2005), 335.
doi: 10.1081/PDE-200050077. |
[14] |
A. Majda and P. E. Souganidis, Flame fronts in a turbulent combustion model with fractal velocity fields,, Comm. Pure Appl. Math., 51 (1998), 1337.
doi: 10.1002/(SICI)1097-0312(199811/12)51:11/12<1337::AID-CPA4>3.0.CO;2-B. |
[15] |
P. Martinez and J.-M. Roquejoffre, Convergence to critical waves in KPP-type equations,, Preprint 2010., (2010). Google Scholar |
[16] |
A. Mellet, J. Nolen, J.-M. Roquejoffre and L. Ryzhik, Stability of generalized transition fronts,, Communications in PDE, 34 (2009), 521.
doi: 10.1080/03605300902768677. |
[17] |
C. Mueller and R. Sowers, Random travelling waves for the KPP equation with noise,, J. Funct. Anal., 128 (1995), 439.
doi: 10.1006/jfan.1995.1038. |
[18] |
J. Nolen, An invariance principle for random traveling waves in one dimension,, SIAM J. Math. Anal., 43 (2011), 153.
doi: 10.1137/090746513. |
[19] |
J. Nolen and L. Ryzhik, Traveling waves in a one-dimensional heterogeneous medium,, AIHP - Analyse Non Linéaire, 26 (2009), 1021.
|
[20] |
J. Nolen and J. Xin, Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows,, AIHP - Analyse Non Linéaire, 26 (2008), 815.
|
[21] |
J. Nolen and J. Xin, KPP fronts in 1D random drift,, Discrete and Continuous Dynamical Systems B, 11 (2009), 421.
doi: 10.3934/dcdsb.2009.11.421. |
[22] |
A. Rocco, U. Ebert and W. van Saarloos, Subdiffusive fluctuations of "pulled" fronts with multiplicative noise,, Phys. Rev. E, 62 (2000).
doi: 10.1103/PhysRevE.62.R13. |
[23] |
W. Shen, Traveling waves in diffusive random media,, J. Dynamics and Diff. Eqns., 16 (2004), 1011.
doi: 10.1007/s10884-004-7832-x. |
[24] |
R. Tribe, A travelling wave solution to the Kolmogorov equation with noise,, Stochastics Stochastics Rep., 56 (1996), 317.
|
[25] |
W. van Saarloos, Front propagation into unstable states,, Physics Reports, 386 (2003), 29.
doi: 10.1016/j.physrep.2003.08.001. |
[26] |
J. Xin, "An Introduction to Fronts in Random Media,", Springer, (2009).
doi: 10.1007/978-0-387-87683-2. |
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