Existence of the harmonic measure for random walks on graphs and in random environments

We give a sufficient condition for the existence of the harmonic measure from infinity of transient random walks on weighted graphs. In particular, this condition is verified by the random conductance model on $\Z^d$, $d\geq 3$, when the conductances are i.i.d. and the bonds with positive conductance percolate. The harmonic measure from infinity also exists for random walks on supercritical clusters of $\Z^2$. This is proved using results of Barlow (2004).Comment: 25 p. and 2 figure

MOA-2020-BLG-135Lb: A New Neptune-class Planet for the Extended MOA-II Exoplanet Microlens Statistical Analysis

We report the light-curve analysis for the event MOA-2020-BLG-135, which leads to the discovery of a new Neptune-class planet, MOA-2020-BLG-135Lb. With a derived mass ratio of $q=1.52_{-0.31}^{+0.39} \times 10^{-4}$ and separation $s\approx1$, the planet lies exactly at the break and likely peak of the exoplanet mass-ratio function derived by the MOA collaboration (Suzuki et al. 2016). We estimate the properties of the lens system based on a Galactic model and considering two different Bayesian priors: one assuming that all stars have an equal planet-hosting probability and the other that planets are more likely to orbit more massive stars. With a uniform host mass prior, we predict that the lens system is likely to be a planet of mass $m_\mathrm{planet}=11.3_{-6.9}^{+19.2} M_\oplus$ and a host star of mass $M_\mathrm{host}=0.23_{-0.14}^{+0.39} M_\odot$, located at a distance $D_L=7.9_{-1.0}^{+1.0}\;\mathrm{kpc}$. With a prior that holds that planet occurrence scales in proportion to the host star mass, the estimated lens system properties are $m_\mathrm{planet}=25_{-15}^{+22} M_\oplus$, $M_\mathrm{host}=0.53_{-0.32}^{+0.42} M_\odot$, and $D_L=8.3_{-1.0}^{+0.9}\; \mathrm{kpc}$. This planet qualifies for inclusion in the extended MOA-II exoplanet microlens sample.Comment: 22 pages, 6 figures, 4 tables, submitted to the AAS Journal

COVID-19 symptoms at hospital admission vary with age and sex: results from the ISARIC prospective multinational observational study

Background: The ISARIC prospective multinational observational study is the largest cohort of hospitalized patients with COVID-19. We present relationships of age, sex, and nationality to presenting symptoms. Methods: International, prospective observational study of 60 109 hospitalized symptomatic patients with laboratory-confirmed COVID-19 recruited from 43 countries between 30 January and 3 August 2020. Logistic regression was performed to evaluate relationships of age and sex to published COVID-19 case definitions and the most commonly reported symptoms. Results: ‘Typical’ symptoms of fever (69%), cough (68%) and shortness of breath (66%) were the most commonly reported. 92% of patients experienced at least one of these. Prevalence of typical symptoms was greatest in 30- to 60-year-olds (respectively 80, 79, 69%; at least one 95%). They were reported less frequently in children (≤ 18 years: 69, 48, 23; 85%), older adults (≥ 70 years: 61, 62, 65; 90%), and women (66, 66, 64; 90%; vs. men 71, 70, 67; 93%, each P < 0.001). The most common atypical presentations under 60 years of age were nausea and vomiting and abdominal pain, and over 60 years was confusion. Regression models showed significant differences in symptoms with sex, age and country. Interpretation: This international collaboration has allowed us to report reliable symptom data from the largest cohort of patients admitted to hospital with COVID-19. Adults over 60 and children admitted to hospital with COVID-19 are less likely to present with typical symptoms. Nausea and vomiting are common atypical presentations under 30 years. Confusion is a frequent atypical presentation of COVID-19 in adults over 60 years. Women are less likely to experience typical symptoms than men

Marches aléatoires sur un amas infini de percolation.

In this thesis, we consider a simple random walk on the infinite cluster of the percolation model on the edges of $\Z^d\ (d\geq 2)$ with law $Q$, in the surcritical case. We look at the Laplace transformation of some functional of local times of this walk. In the first part, we investigate the particular case of the Laplace transformation of the number of visited sites up to time $n$, called $N_n$. We prove that this quantity has the same behaviour as the random walk on $\Z^d$. More precisely, we show for all $00$ such that for almost all realisations ofthe percolation such that the origin belongs to the infinite cluster and for large enough $n$, e^{-C_i n^{ \frac{d}{d+2} } } \leq \E_0^{\omega} ( \alpha^{N_n} ) \leq e^{-C_sn^{ \frac{d}{d+2} }}. In the second part, we extend this kind of estimate for other functionals. For these problems, the main work is to get the upper bound. Our approach is based, first on finding an isoperimetric inequality on the infinite cluster and secondly to lift it on a wreath product, which enables us to get an upper bound of the return probability of a particular random walk on this wreath product. The introduction of a wreath product is motivated by the fact that the return probability on such graph is linked to the Laplace transform of some functional of the locals times for a good choice of the fibers. Finally, in the last part we explain with details and in a general case, following ideas of A.Erschler, how to get a isoperimetric inequality on a wreath product of two graphs from an isoperimetric inequality on each graphs.Dans cette thèse, on s'intéresse à une marche aléatoire simplesur un amas infini issu d'un processus de percolation surcritique sur les arêtes de $\Z^d \ (d \geq 2)$ de loi $Q$. On étudie des transformées de Laplace de certaines fonctionnelles des temps locaux de cette marche. Dans une première partie, on s'intéresse au cas particulier de la transformée de Laplace du nombre de points visités au temps $n$, noté $N_n$. On montre notamment que cette quantité a un comportement similaire au cas où la marche évolue dans $\Z^d$. Plus précisément, on établit que pour tout $00$ telles que pour presque toute réalisation de la percolation telle que l'origine appartienne à l'amas infini et pour $n$ assez grand, e^{-C_i n^{ \frac{d}{d+2} } } \leq \E_0^{\omega} ( \alpha^{N_n} ) \leq e^{-C_sn^{ \frac{d}{d+2} }}. Dans une seconde partie, on généralise ce type d'estimées pour d'autres fonctionnelles. Dans ce type de problème, le point principal du travail réside dans l'obtention de la borne supérieure. Notre approche consiste dans un premier temps, à trouver une famille d'inégalité isopérimétrique sur l'amas infini, et dans un deuxième temps à la remonter sur un produit en couronne, ce qui nous permet alors d'obtenir une majoration de la probabilité de retour d'une certaine marche sur ce produit en couronne. L'introduction d'un produit en couronne est justement motivée par le fait que la probabilité de retour sur un tel graphe peut s'interprèter comme l'espérance de la transformée de Laplace de certaines fonctionnelles des temps locaux pour un bon choix des fibres. Enfin, dans la dernière partie, il est expliqué en détail et de manière générale, en suivant la stratégie d'A. Erschler, comment obtenir une inégalité isopérimétrique sur un produit en couronne de deux graphes à partir d'inégalité isopérimétrique de chacun des deux graphes

Existence of graphs with sub exponential transitions probability decay and applications

International audienceIn this paper, we recall the existence of graphs with bounded valency such that the simple random walk has a return probability at time n at the origin of order exp(-n(alpha)), for fixed alpha is an element of [0, 1] and with Folner function exp(n 2 alpha/1-alpha). This result was proved by Erschler (see [4], [3]); we give a more detailed proof of this construction in the appendix. In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random walk on an infinite cluster on the percolation model

Les effets de la consultation avec les riverains sur la prévention des risques industriels

International audienceThis article models the collaboration between high-risk (hazardous) industries and residents on the safety investments to be implemented. We compare the safety investments level implemented by the company when it decides alone and when there is consultation with residents within the SMC (Site Monitoring Commissions). It appears that companies are likely to increase their investment effort when they consult with the residents. However, although this collaboration with citizens still seems insufficient in the eyes of residents' associations, the consideration of citizen's point of view via a review of accident probabilities does not necessarily have a favorable impact on safety investments. That is why it is necessary to go beyond the limits imposed by the probabilistic approach

A NOTE ON EXIT TIME FOR ANCHORED ISOPERIMETRY

International audienceLet (Xn) n≥0 be a reversible random walk on a graph G satisfying an anchored isoperimetric inequality. We give upper bounds for exit time (and occupation time in transient case) by X of any set which contains the root. This article covers many results of [11].Soit (Xn) n≥0 une marche aléatoire réversible sur un graphe G vérifiant une inégalité isopérimétrique ancrée. Nous obtenons une majoration du temps de sortie de tout ensemble connexe contenant un point ancre (et du temps de passage dans le cas transient) de la marche X. Cet article reprend un grand nombre de résultats de [11]

Les investissements de sécurisation des sites industriels à risque et la concertation entre firmes et riverains: une approche théorique

International audienceCet article propose une modélisation de la concertation entre industries à risque et riverains sur les investissements de sécurité à mettre en œuvre. Le modèle permet de déterminer à quel niveau se fixent le taux de profit espéré et le taux d’investissement de sécurisation à mettre en œuvre. Nous mettons en évidence les déterminants des investissements de sécurisation et montrons que l’intérêt des riverains, favorables à plus de sécurité, n’est pas forcément incompatible avec l’intérêt de la firme : une exigence plus grande des riverains en matière de sécurité peut s’accompagner d’une hausse simultanée de l’investissement de sécurisation et du taux de profit espéré. Nous suggérons alors le développement de la logique de concertation, et la nécessité de rendre la concertation plus équilibrée en permettant aux riverains de commander des contre-expertises en matière d’études de danger

Marches aléatoires sur un amas de percolation

Dans cette these, on s interesse a une marche aleatoire simple sur un amas infini issu d un processus de percolation surcritique sur les aretes de Zd (d >= 2) de loi Q. On etudie des transformees de Laplace de certaines fonctionnelles des temps locaux de cette marche. Dans une premiere partie, on s interesse au cas particulier de la transformee de Laplace du nombre de points visites au temps n, note Nn. On montre notamment que cette quantite a un comportement similaire au cas ou la marche evolue dans Zd. Plus precisement, on etablit que pour tout 0 0 telles que pour presque toute realisation de la percolation telle que l origine appartienne a l amas infini et pour n assez grand, e Cin d/d+2=2) with law Q, in the surcritical case. We look at the Laplace transformation of some functional of local times of this walk. In the first part, we investigate the particular case of the Laplace transformation of the number of visited sites up to time n, called Nn. We prove that this quantity has the same behaviour as the random walk on Zd. More precisely, we show for all 0 0 such that for almost all realisations of the percolation such that the origin belongs to the infinite cluster and for large enough n, e Cin d d+2 <= E [oméga]0 (a Nn) <=e Csn d d+2. In the second part, we extend this kind of estimate for other functionals. For these problems, the main work is to get the upper bound. Our approach is based, first on finding an isoperimetric inequality on the infinite cluster and secondly to lift it on a wreath product, which enables us to get an upper bound of the return probability of a particular random walk on this wreath product. The introduction of a wreath product is motivated by the fact that the return probability on such graph is linked to the Laplace transform of some functional of the locals times for a good choice of the fibers. Finally, in the last part we explain with details and in a general case, following ideas of A.Erschler, how to get a isoperimetric inequality on a wreath product of two graphs from an isoperimetric inequality on each graphs.AIX-MARSEILLE1-Inst.Médit.tech (130552107) / SudocSudocFranceF