All issues Volume 26 (2022) ESAIM: PS, 26 (2022) 397-435 References
O. Arino, A survey of structured cell population dynamics. Acta Biotheor. 43 (1995) 3–25. [CrossRef] [PubMed] [Google Scholar]
S. Asmussen and H. Hering Strong limit theorems for general supercritical branching processes with applications to branching diffusions. Zeitsch. Wahrscheinlichkeitstheorie Verwandte Gebiete 36 (1976) 195–212. [Google Scholar]
K.B. Athreya Limit theorems for multitype continuous time Markov branching processes. Zeitsch. Wahrscheinlichkeitstheorie Verwandte Gebiete 12 (1969) 320–332. [Google Scholar]
W. Balmant, M.H. Sugai-Guérios, J.H. Coradin, N. Krieger, A.F. Junior and D.A. Mitchell, A model for growth of a single fungal hypha based on well-mixed tanks in series: simulation of nutrient and vesicle transport in aerial reproductive hyphae. PLoS One 10 (2015) e0120307. [Google Scholar]
J. Banasiak, K. Pichér and R. Rudnicki Asynchronous exponential growth of a general structured population model. Acta Appl. Math. 119 (2012) 149–166. [CrossRef] [MathSciNet] [Google Scholar]
V. Bansaye, B. Cloez, P. Gabriel and A. Marguet, A non-conservative Harris' ergodic theorem. To appear in J. London Math. Soc. arXiv:1903.03946 (2019). [Google Scholar]
V. Bansaye, J.-F. Delmas, L. Marsalle and V.C. Tran Limit theorems for Markov processes indexed by continuous time Galton-Watson trees. Ann. Appl. Probab. 21 (2011) 2263–2314. [CrossRef] [MathSciNet] [Google Scholar]
D.J. Barry and G.A. Williams Microscopic characterisation of filamentous microbes: towards fully automated morphological quantification through image analysis. J. Microsc. 244 (2011) 1–20. [Google Scholar]
J. Bertoin and A.R. Watson, A probabilistic approach to spectral analysis of growth-fragmentation equations. J. Funct. Anal. 274 (2018) 2163–2204. [Google Scholar]
L. Boddy, J. Wood, E. Redman, J. Hynes and M.D. Fricker Fungal network responses to grazing. Fungal Genet. Biol. 47 (2010) 522–530. [CrossRef] [Google Scholar]
G.P. Boswell and F.A. Davidson Modelling hyphal networks. Fungal Biol. Rev. 26 (2012) 30–38. [CrossRef] [Google Scholar]
F. Brikci, J. Clairambault and B. Perthame Analysis of a molecular structured population model with possible polynomial growth for the cell division cycle. Math. Comput. Modell. 47 (2008) 699–713. [Google Scholar]
J. Calvo, M. Doumic and B. Perthame Long-time asymptotics for polymerization models. Commun. Math. Phys. 363 (2018) 111–137. [CrossRef] [Google Scholar]
J.A. Canizo, P. Gabriel and H. Yoldas Spectral gap for the growth-fragmentation equation via Harris's Theorem. SIAM J. Math. Anal. 53 (2021) 5185–5214. [Google Scholar]
V. Capasso and F. Flandoli On the mean field approximation of a stochastic model of tumour-induced angiogenesis. Eur. J. Appl. Math. 30 (2019) 619–658. [CrossRef] [Google Scholar]
R. Catellier, Y. D'Angelo and C. Ricci, A mean-field approach to self-interacting networks, convergence and regularity. Math. Models Methods Appl. Sci. 31 (2021) 2597–2641. [Google Scholar]
B. Chauvin Sur la propriéetée de branchement. Ann. IHP Probab. Statist. 22 (1986) 233–236. [Google Scholar]
B. Cloez Limit theorems for some branching measure-valued processes. Adv. Appl. Probab. 49 (2017) 549–580. [Google Scholar]
B. Cloez, B. de Saporta and T. Roget Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process. J. Math. Biol. 83 (2021) 1–30. [Google Scholar]
J. Dikec, A. Olivier, C. Bobéee, Y. D'Angelo, R. Catellier, P. David, F. Filaine, S. Herbert, C. Lalanne, H. Lalucque, L. Monasse, M. Rieu, G. Ruprich-Robert, A. Véeber, F. Chapeland-Leclerc and E. Herbert, Hyphal network whole field imaging allows for accurate estimation of anastomosis rates and branching dynamics of the filamentous fungus Podospora anserine. Sci. Rep. 10 (2020) 3131. [Google Scholar]
M. Doumic, A. Olivier and L. Robert, Estimating the division rate from indirect measurements of single cells. ArXiv preprint arXiv:1907.05108 (2019). [Google Scholar]
H. Du, M. Ayouz, P. Lv and P. Perrée, A lattice-based system for modeling fungal mycelial growth in complex environments. Physica A 511 (2018) 191–206. [Google Scholar]
H. Du, T.-B.-T. Tran and P. Perrée, A 3-variable PDE model for predicting fungal growth derived from microscopic mechanisms. J. Theor. Biol. 470 (2019) 90–100. [Google Scholar]
J. Engländer, S.C. Harris and A.E. Kyprianou Strong law of large numbers for branching diffusions. Ann. l'I.H.P. Probab. Stat. 46 (2010) 279–298. [Google Scholar]
M. Fricker, L. Heaton, N. Jones and L. Boddy The Mycelium as a Network. Microbiol. Spectr. 5 (2017) 3131. [Google Scholar]
L. Heaton, B. Obara, V. Grau, N. Jones, T. Nakagaki, L. Boddy and M.D. Fricker Analysis of fungal networks. Fungal Biol. Rev. 26 (2012) 12–29. [CrossRef] [Google Scholar]
H. Kesten and B.P. Stigum, A Limit Theorem for Multidimensional Galton-Watson Processes, Ann. Math. Statist. 37 (1966) 1211–1223. [CrossRef] [MathSciNet] [Google Scholar]
A. Lamour, F. Van Den Bosch, A.J. Termorshuizen and M.J. Jeger, Modelling the growth of soil-borne fungi in response to carbon and nitrogen. IMA J. Math. Appl. Med. Biol. 17 (2000) 329–346. [CrossRef] [Google Scholar]
A. Marguet Uniform sampling in a structured branching population. Bernoulli 25 (2019) 2649–2695. [Google Scholar]
S. Mischler and J. Scher Spectral analysis of semigroups and growth-fragmentation equations. Ann. l'Institut Henri Poincare (C) Non Linear Anal. 33 (2016) 849–898. [CrossRef] [Google Scholar]
E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators. Cambridge Tracts in Mathematics, Cambridge University Press (1984). [Google Scholar]
B. Perthame, Transport equations in biology. Springer Science and Business Media (2006). [Google Scholar]
S.H. Tindemans, N. Kern and B.M. Mulder The diffusive vesicle supply center model for tip growth in fungal hyphae. J. Theor. Biol. 238 (2006) 937–948. [Google Scholar]
V.C. Tran Large population limit and time behaviour of a stochastic particle model describing an age-structured population. ESAIM: PS 12 (2008) 345–386. [CrossRef] [EDP Sciences] [Google Scholar]