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27/01/2025 08:30
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Lisa Hartung27/01/2025 09:00
In this minicourse, I will explain how Feynman-Kac formulas can be used to solve Fisher-Kolmogorov-Petrovsky-Pikunov equations (F-KPP). Maury Bramson first used this approach in his seminal paper on the F-KPP equation about 50 years ago. We will revisit his approach and then also apply this technique to systems of F-KPP equations. Moreover, I will explain the duality between (certain) F-KPP...
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Patricia Reynaud-Bouret27/01/2025 10:40
I will give an introductory course on point processes that are used to model nueornal activity in the brain. I will especially focus on Hawkes processes even if I will recall some basic notions on Poisson processes as well. I will review the various methods to simulate such networks when the size is huge and comparable to animal brains or brain areas. A new algorithm especially involves...
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Serte Donderwinkel27/01/2025 14:00
We consider a branching random walk whose genealogy is given by the family tree of a Bienaymé branching process conditioned to have n vertices. Think of this model as a random tree in which each vertex has a spatial location that is given by the position of its parent plus its own random displacement.
In the first lecture, we will consider the convergence under rescaling of the underlying...
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Lisa Hartung27/01/2025 15:40
In this minicourse, I will explain how Feynman-Kac formulas can be used to solve Fisher-Kolmogorov-Petrovsky-Pikunov equations (F-KPP). Maury Bramson first used this approach in his seminal paper on the F-KPP equation about 50 years ago. We will revisit his approach and then also apply this technique to systems of F-KPP equations. Moreover, I will explain the duality between (certain) F-KPP...
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27/01/2025 17:00
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Patricia Reynaud-Bouret (Université Côte d'Azur, CNRS, LJAD)28/01/2025 09:00
I will give an introductory course on point processes that are used to model nueornal activity in the brain. I will especially focus on Hawkes processes even if I will recall some basic notions on Poisson processes as well. I will review the various methods to simulate such networks when the size is huge and comparable to animal brains or brain areas. A new algorithm especially involves...
Aller à la page de la contribution -
Serte Donderwinkel28/01/2025 10:40
We consider a branching random walk whose genealogy is given by the family tree of a Bienaymé branching process conditioned to have n vertices. Think of this model as a random tree in which each vertex has a spatial location that is given by the position of its parent plus its own random displacement.
In the first lecture, we will consider the convergence under rescaling of the underlying...
Aller à la page de la contribution -
Lisa Hartung28/01/2025 13:30
In this minicourse, I will explain how Feynman-Kac formulas can be used to solve Fisher-Kolmogorov-Petrovsky-Pikunov equations (F-KPP). Maury Bramson first used this approach in his seminal paper on the F-KPP equation about 50 years ago. We will revisit his approach and then also apply this technique to systems of F-KPP equations. Moreover, I will explain the duality between (certain) F-KPP...
Aller à la page de la contribution -
Patricia Reynaud-Bouret (Université Côte d'Azur, CNRS, LJAD)28/01/2025 15:00
I will give an introductory course on point processes that are used to model nueornal activity in the brain. I will especially focus on Hawkes processes even if I will recall some basic notions on Poisson processes as well. I will review the various methods to simulate such networks when the size is huge and comparable to animal brains or brain areas. A new algorithm especially involves...
Aller à la page de la contribution -
Serte Donderwinkel28/01/2025 16:20
We consider a branching random walk whose genealogy is given by the family tree of a Bienaymé branching process conditioned to have n vertices. Think of this model as a random tree in which each vertex has a spatial location that is given by the position of its parent plus its own random displacement.
In the first lecture, we will consider the convergence under rescaling of the underlying...
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Quentin Berger (Sorbonne Université)29/01/2025 09:00
Some statistical mechanics models on trees may sometimes reduce to the study of some "simple" tree recursion; this is for instance the case for the Ising model and FK-percolation model. It turns out that when the recursion is concave, we can compare this tree recursion to the one verified by (possibly non-linear) resistive networks.
I will present some recent work with Irene Ayuso Ventura...
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Irene Ayuso Ventura (Durham University)29/01/2025 09:45
We study the Ising model on a Galton-Watson tree with a random external field, which can be interpreted as randomly introducing "interfering vertices" with a fixed spin. This model is motivated by the study of the Ising model on tree-like random graphs, which can serve as a framework for understanding cooperative behaviour in social networks. In joint work with Quentin Berger (Sorbonne Nord),...
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Matteo D'Achille (Laboratoire de Mathématiques d’Orsay, Université Paris-Saclay)29/01/2025 10:45
Series-Sinai have shown in the nineties that the ferromagnetic n.n. Ising model defined on the Cayley graph of a co-compact group of isometries of the hyperbolic plane $\mathbb{H}_2$ exhibits uncountably many, mutually singular Gibbs states at very low temperature ---one for every bi-infinite geodesic of $\mathbb{H}_2$.
They also conjectured the extremality of their states but the problem...
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M. Yueyun Hu29/01/2025 11:30
This talk is based on a joint work with Eile Aïdékon and Zhan Shi. Let $(V(u),\, u\in T)$ be a (supercritical) branching random walk and $(\eta_u,\,u\in T)$ be positive marks on the vertices of the tree, distributed in an i.i.d. fashion. Following Aldous and Bandyopadhyay (2005), for each infinite ray $\xi$ of the tree, we associate the {\it discounted tree sum} $D(\xi)$ which is the sum of...
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M. Guilhem Semerjian29/01/2025 14:00
This talk will present some results on the planted matching problem, an inference problem where the goal is to recover a perfect matching hidden (planted) in a weighted graph, the weights on the planted and non-planted edges being drawn from two different distributions. The results are obtained with statistical mechanics techniques, and in particular a mapping to branching random walks....
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M. Liu Quansheng29/01/2025 14:45
In this talk, I will present some recent progress in the study of products of positive random matrices and branching processes in random environments. In particular, a Perron-Frobenius type theorem and stable convergence theorem for products of positive random matrices, and a Bahadur-Rao type precise large deviation result for multitype branching processes in random environments, will be...
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M. William DA SILVA29/01/2025 15:45
We study the branching structure induced by a space-filling SLE(6) exploration of the quantum disc with matching parameter. We prove that it can be described as one of the growth-fragmentation processes introduced by Bertoin, Budd, Curien and Kortchemski in the context of planar maps. Importantly, our arguments are elementary, relying only on planar Brownian motion, and requiring no prior...
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M. Jean-François Le Gall29/01/2025 16:30
Brownian motion indexed by the Brownian tree appears in the
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asymptotics of many models of combinatorics or statistical physics,
and is also closely related to super-Brownian motion. We
consider the process of local times of (one-dimensional) Brownian motion
indexed by the Brownian tree and we show that, although this
process is not Markov, the pair formed by the local time and
its... -
Jean-Michel Roquejoffre30/01/2025 09:45
The question under study, at large intermediate times, of a system,
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proposed by the economists Lucas and Moll, aimed at describing the growth of an economy by means of diffusion of knowledge. The individual agents in the economy are supposed to share their time between learning and producing. They advance their knowledge by
learning from each other and via internal innovation, and their... -
M. Claude Godrèche30/01/2025 10:45
The distribution of the first positive position reached by a random walker starting from the origin plays a fundamental role in describing the statistics of extremes and records in one-dimensional random walks.
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We present a comprehensive study of this distribution, with a particular focus on its moments and asymptotic behaviour, in the case where the step distribution is continuous and... -
Pierre Le Doussal30/01/2025 11:30
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Manon Costa (Institut de Mathématiques de Toulouse)30/01/2025 14:00
Dans cet exposé, je présenterai quelques résultats récents sur le comportement à long terme des processus de Hawkes inhibés, à la fois en temps continu et en temps discret. En particulier, nous soulignerons le rôle complexe de l'inhibition dans la stabilité des processus de Hawkes.
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Julie Tourniaire (Université de Franche-Comté)30/01/2025 14:45
The FKPP equation is a common model in population dynamics, describing how a population spreads and grows over time and space, resulting in wave-like patterns.
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Recent studies by Birzu, Hallatschek and Korolev on the noisy FKPP equation with Allee effects (or cooperation) suggest the existence of three classes of fluctuating wavefronts: pulled, semipushed and fully pushed fronts.
In this... -
Jean-Jil Duchamps (Université de Franche-Comté, Besançon, France)30/01/2025 15:45
Some models of discrete-time epidemics can be studied in the larger setting of first-passage percolation in multitype directed configuration models, where edges have an integer length representing transmission delays. Through directed breadth-first explorations and coupling with multitype branching processes on countable state spaces, we study the distribution of geodesics between several...
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Alejandro Hernandez Wences (LAAS - CNRS)30/01/2025 16:30
In this joint project with Arno Siri-Jégousse, we introduce a novel research program connecting the fields of mathematical population genetics and self-similar (SS) Markov processes in infinite dimensions. Specifically, we propose a shift in focus from the prevalent paradigm based on the branching property as a tool to analyze the structure of population models, to one based on the...
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Anita Winter31/01/2025 09:00
The CRT is the scaling limit of the UST on the complete graph. The Aldous-Broder chain on a graph G=(V,E) is a MC with values in the space of rooted trees with vertices in V that is invariant under the uniform distribution on the space of rooted trees spanning G. In Evans, Pitman and Winter (2006) the so-called root growth with regrafting process (RGRG) was constructed. It was further shown...
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Eleanor Archer31/01/2025 09:45
We consider critical percolation on a supercritical Galton- Watson tree with mean offspring m > 1. It is well known that the critical percolation probability for this model is 1/m and that the root cluster has the distribution of a critical Galton-Watson tree. For this reason, many properties of the cluster are well understood, such as aymptotics for long range survival probabilities, the size...
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Marie Doumic31/01/2025 10:45
The depolymerization (i.e. progressive shortening) of large molecules can be modeled by discrete Becker-Döring-type equations, or by continuous equations. In many applications, the dynamic nature of the experiments, as well as their nanometric scale, makes it difficult to estimate quantitatively, or even simply to decipher the mechanisms involved.
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In this talk, I will discuss two problems... -
Nicolas Broutin31/01/2025 11:30
Je présenterai une manière de construire des arbres aléatoires basée sur les minorants convexes de fonctions (aléatoires). Dans le cas Brownien, cette procédure est reliée au coalescent additif et à l'arbre continu Brownien, c'est-à-dire la limite d'échelle d'arbres uniformes, et de la fragmentation naturelle qui consiste à retirer les arêtes dans un ordre aléatoire.
En modifiant un peu la...
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Bertrand CLOEZ
In this talk, we consider branching processes in infinite dimension; that is, a particle system where each particle follows Markov dynamics independently of the others between particle birth and death events. This includes growth-fragmentation processes, branching diffusions, Bellman-Harris processes... We will present recent results on the laws of large numbers and central limit theorems for...
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