F. Achleitner and C. Kuehn, Traveling waves for a bistable equation with nonlocal-diffusion

S. M. Allen and J. W. Cahn, A microscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metallurgica, vol.27, issue.6, pp.1085-1905, 1979.
DOI : 10.1016/0001-6160(79)90196-2

L. Arnold, Random Dynamical Systems, 2003.

N. Berglund, G. D. Gesù, and H. Weber, An Eyring-Kramers law for the stochastic Allen- Cahn equation in dimension two, pp.1-26, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01304559

N. Berglund and C. Kuehn, Regularity structures and renormalisation of FitzHugh???Nagumo SPDEs in three space dimensions, Electronic Journal of Probability, vol.21, issue.18, pp.1-48, 2016.
DOI : 10.1214/16-EJP4371
URL : https://hal.archives-ouvertes.fr/hal-01141380

D. Blömker, Amplitude Equations for Stochastic Partial Differential Equations, World Scientific, vol.3, 2007.
DOI : 10.1142/6440

N. Broutin and P. Flajolet, The distribution of height and diameter in random non-plane binary trees, Random Structures & Algorithms, vol.4, issue.2, pp.215-252, 2012.
DOI : 10.1002/rsa.20393
URL : https://hal.archives-ouvertes.fr/hal-00773369

Y. Bruned, M. Hairer, and L. Zambotti, Algebraic renormalisation of regularity structures, pp.1-84, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01389938

A. Chandra and M. Hairer, An analytic BPHZ theorem for regularity structures, pp.1-113, 2016.

A. Chandra and H. Weber, Stochastic PDEs, regularity structures, and interacting particle systems, 2015.

Z. Chen, P. Kim, and R. Song, Heat kernel estimates for the Dirichlet fractional Laplacian, Journal of the European Mathematical Society, vol.12, pp.1307-1329, 2010.
DOI : 10.4171/JEMS/231

M. C. Cross and P. C. Hohenberg, Pattern formation outside of equilibrium, Reviews of Modern Physics, vol.65, issue.3, pp.851-1112, 1993.
DOI : 10.1103/RevModPhys.65.851

C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, 2010.

B. Fish, R. Kushwaha, and G. Turan, Betweenness centrality profiles in trees, pp.1-21, 2016.

R. A. Fisher, THE WAVE OF ADVANCE OF ADVANTAGEOUS GENES, Annals of Eugenics, vol.7, issue.4, pp.353-369, 1937.
DOI : 10.1111/j.1469-1809.1937.tb02153.x

P. K. Friz and M. Hairer, A Course on Rough Paths: With an Introduction to Regularity Structures, 2014.
DOI : 10.1007/978-3-319-08332-2

C. Gardiner, Stochastic Methods, 2009.

M. Gubinelli, Controlling rough paths, Journal of Functional Analysis, vol.216, issue.1, pp.86-140, 2004.
DOI : 10.1016/j.jfa.2004.01.002
URL : http://doi.org/10.1016/j.jfa.2004.01.002

M. Gubinelli, P. Imkeller, and N. Perkowski, PARACONTROLLED DISTRIBUTIONS AND SINGULAR PDES, Forum of Mathematics, Pi, vol.1908, p.6, 2015.
DOI : 10.4171/RMI/240

M. Gubinelli and S. Tindel, Rough evolution equations, The Annals of Probability, vol.38, issue.1, pp.1-75, 2010.
DOI : 10.1214/08-AOP437
URL : https://hal.archives-ouvertes.fr/hal-00359724

M. Hairer, Solving the KPZ equation, Annals of Mathematics, vol.178, issue.2, pp.559-664, 2013.
DOI : 10.4007/annals.2013.178.2.4

M. Hairer, A theory of regularity structures, Inventiones mathematicae, vol.67, issue.1, pp.269-504, 2014.
DOI : 10.1007/s00222-014-0505-4

M. Hairer, The motion of a random string, pp.1-20, 2015.

M. Hairer, Regularity structures and the dynamical $\Phi^4_3$ model, Current Developments in Mathematics, vol.2014, issue.1, pp.1-46, 2015.
DOI : 10.4310/CDM.2014.v2014.n1.a1

M. Hairer and H. Weber, Large deviations for white-noise driven, nonlinear stochastic PDEs in two and three dimensions, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.24, issue.1, pp.55-92, 2015.
DOI : 10.5802/afst.1442

R. Hoyle, Pattern Formation: An Introduction to Methods, 2006.
DOI : 10.1017/CBO9780511616051

M. Kardar, G. Parisi, and Y. C. Zhang, Dynamic Scaling of Growing Interfaces, Physical Review Letters, vol.56, issue.9, pp.889-892, 1986.
DOI : 10.1103/PhysRevLett.56.889

R. Klages, G. Radons, and I. M. Sokolov, Anomalous Transport: Foundations and Applications, 2008.
DOI : 10.1002/9783527622979

A. Kolmogorov, I. Petrovskii, and N. Piscounov, A study of the diffusion equation with increase in the amount of substance, and its application to a biological problem, Kluwer, vol.1, pp.248-270, 1937.

Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, 2004.

M. Kwa´snickikwa´snicki, Ten equivalent definitions of the fractional Laplace operator, pp.1-31, 2015.

R. Metzler and J. Klafter, The random walk's guide to anomalous diffusion: a fractional dynamics approach, Physics Reports, vol.339, issue.1, pp.1-77, 2000.
DOI : 10.1016/S0370-1573(00)00070-3

J. Nagumo, S. Arimoto, and S. Yoshizawa, An Active Pulse Transmission Line Simulating Nerve Axon, Proc. IRE, pp.2061-2070, 1962.
DOI : 10.1109/JRPROC.1962.288235

R. Otter, The Number of Trees, The Annals of Mathematics, vol.49, issue.3, pp.583-599, 1948.
DOI : 10.2307/1969046

L. Page, S. Brin, R. Motwani, and T. Winograd, The PageRank citation ranking: bringing order to the web, pp.1-17, 1999.

G. Da-prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, 1992.

K. Sato, Lévy Processes and Infinitely Divisible Distributions. CUP, 1999. Nils Berglund Université d

B. Bâtiment-de-mathématiques, P. 6759 45067 Orléans Cedex 2, France E-mail address: nils.berglund@univ-orleans