Sharp ellipticity conditions for ballistic behavior of random walks in random environment

We sharpen ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ram\'{\i}rez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of Berger, Drewitz and Ram\'{\i}rez. As a corollary, we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension $d=2$ under which the corresponding random walk is ballistic.Comment: Published at http://dx.doi.org/10.3150/14-BEJ683 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Sharp ellipticity conditions for ballistic behavior of random walks in random environment

We sharpen the ellipticity criteria for random walks in i.i.d. random environments introduced by Campos and Ramírez which ensure ballistic behavior. Furthermore, we construct new examples of random environments for which the walk satisfies the polynomial ballisticity criteria of Berger, Drewitz and Ramírez. As a corollary we can exhibit a new range of values for the parameters of Dirichlet random environments in dimension $d=2$ under which the corresponding random walk is ballistic

A quenched functional central limit theorem for random walks in random environments under (T)gamma(T)_gamma

We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently under the assumption of large finite moments for the regeneration times. In this paper, we relax these moment assumptions under Sznitman's (T)γ ballisticity condition, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments

A quenched functional central limit theorem for random walks in random environments under (T)[gamma]

We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently under the assumption of large finite moments for the regeneration times. In this paper, we relax these moment assumptions under Sznitman's (T)γ ballisticity condition, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments

DOI: 10.1214/EJP.v18-2109 SUB-BALLISTIC RANDOM WALK IN DIRICHLET ENVIRONMENT

Abstract. We consider random walks in Dirichlet environment (RWDE) on Z d, for d � 3, in the sub-ballistic case. We associate to any parameter (α1,...,α2d) of the Dirichlet law a time-change to accelerate the walk. We prove that the continuoustime accelerated walk has an absolutely continuous invariant probability measure for the environment viewed from the particle. This allows to characterize directional transience for the initial RWDE. It solves as a corollary the problem of Kalikow’s0−1 law in the Dirichlet case in any dimension. Furthermore, we find the polynomial order of the magnitude of the original walk’s displacement. hal-00701531, version 1- 25 May 2012 1

Marches aléatoires en environnement aléatoire faiblement elliptique

In this thesis we study random walks in random environment on Zd. We are particularly interested in environments that are elliptic, but not uniformly elliptic. Those environments can contain traps on which the walk spends a lot of time. The first results in this thesis (chapter 4) deal with the particular case of Dirichlet environments. Random walks in Dirichlet environment form a sub-class of random walks in random environment with specific properties. We consider dimensions d 3 and we study the behavior of the walk when the traps created by the non-uniform ellipticity play an important part. In this context, we show the equivalence between the static and dynamic points of view for an accelerated walk. This completes the results of directional transience and recurrence obtained by Sabot, and it allows to find the polynomial order of the magnitude of the walk’s displacement in the sub-ballistic transient case. Then (chapter 5) we consider the case of directionally transient walks, and we study the conditions on the law of the environment that ensure the existence of moments for the regeneration times. We thus improve the results obtained by Campos and Ramírez. In the last section (chapter 6), we consider the case of ballistic random walks and we study the conditions under which a quenched central limit theorem holds. Under the additional assumption (T), we weaken the integrability of the regeneration times necessary for the works of Rassoul- Agha and Seppäläinen, and Berger and Zeitouni. We obtain the condition E (τ12+ε) < +∞ (whereas for the annealed theorem, the optimal condition is E (τ12) < +∞)Cette thèse est dédiée à l'étude des marches aléatoires en milieu aléatoire sur Zd. On s'intéresse tout particulièrement aux environnements qui sont elliptiques, mais pas uniformément elliptiques, et qui peuvent donc contenir des pièges sur lesquels la marche passe beaucoup de temps. Le premier résultat de cette thèse (chapitre 4) concerne les environnements de Dirichlet, qui forment une sous-classe de marches aléatoires en milieu aléatoire présentant des propriétés remarquables. On se place en dimension d≥ 3 et on étudie le cas où les pièges dus à la non-uniforme ellipticité sont prépondérants. Dans ce contexte, on montre l'équivalence des points de vue statique et dynamique pour une marche accélérée. Ceci permet de compléter les résultats de transience et récurrence directionnelles obtenus par Sabot, et de donner le degré polynomial de l'éloignement de la marche par rapport à l'origine dans le cas sous-balistique et transient. On se place ensuite (chapitre 5) dans le cas des marches transientes dans une direction, et on étudie les conditions sur la loi de l'environnement nécessaires pour assurer l'existence de moments pour les temps de renouvellement. On améliore ainsi les résultats obtenus par Campos et Ramírez. Dans la dernière partie (chapitre 6), on étudie les conditions d'application du théorème central limite quenched dans le cas des marches aléatoires balistiques. Sous la condition supplémentaire (T), on affaiblit les hypothèses sur l'intégrabilité des temps de renouvellement des travaux de Rassoul-Agha et Seppäläinen et de Berger et Zeitouni : on arrive à la condition E (τ12+ε) < +∞ (pour le théorème annealed la condition optimale est E (τ12) < +∞

Random walks in weakly elliptic random environment

Cette thèse est dédiée à l'étude des marches aléatoires en milieu aléatoire sur Zd. On s'intéresse tout particulièrement aux environnements qui sont elliptiques, mais pas uniformément elliptiques, et qui peuvent donc contenir des pièges sur lesquels la marche passe beaucoup de temps. Le premier résultat de cette thèse (chapitre 4) concerne les environnements de Dirichlet, qui forment une sous-classe de marches aléatoires en milieu aléatoire présentant des propriétés remarquables. On se place en dimension d≥ 3 et on étudie le cas où les pièges dus à la non-uniforme ellipticité sont prépondérants. Dans ce contexte, on montre l'équivalence des points de vue statique et dynamique pour une marche accélérée. Ceci permet de compléter les résultats de transience et récurrence directionnelles obtenus par Sabot, et de donner le degré polynomial de l'éloignement de la marche par rapport à l'origine dans le cas sous-balistique et transient. On se place ensuite (chapitre 5) dans le cas des marches transientes dans une direction, et on étudie les conditions sur la loi de l'environnement nécessaires pour assurer l'existence de moments pour les temps de renouvellement. On améliore ainsi les résultats obtenus par Campos et Ramírez. Dans la dernière partie (chapitre 6), on étudie les conditions d'application du théorème central limite quenched dans le cas des marches aléatoires balistiques. Sous la condition supplémentaire (T), on affaiblit les hypothèses sur l'intégrabilité des temps de renouvellement des travaux de Rassoul-Agha et Seppäläinen et de Berger et Zeitouni : on arrive à la condition E (τ12+ε) < +∞ (pour le théorème annealed la condition optimale est E (τ12) < +∞)In this thesis we study random walks in random environment on Zd. We are particularly interested in environments that are elliptic, but not uniformly elliptic. Those environments can contain traps on which the walk spends a lot of time. The first results in this thesis (chapter 4) deal with the particular case of Dirichlet environments. Random walks in Dirichlet environment form a sub-class of random walks in random environment with specific properties. We consider dimensions d 3 and we study the behavior of the walk when the traps created by the non-uniform ellipticity play an important part. In this context, we show the equivalence between the static and dynamic points of view for an accelerated walk. This completes the results of directional transience and recurrence obtained by Sabot, and it allows to find the polynomial order of the magnitude of the walk’s displacement in the sub-ballistic transient case. Then (chapter 5) we consider the case of directionally transient walks, and we study the conditions on the law of the environment that ensure the existence of moments for the regeneration times. We thus improve the results obtained by Campos and Ramírez. In the last section (chapter 6), we consider the case of ballistic random walks and we study the conditions under which a quenched central limit theorem holds. Under the additional assumption (T), we weaken the integrability of the regeneration times necessary for the works of Rassoul- Agha and Seppäläinen, and Berger and Zeitouni. We obtain the condition E (τ12+ε) < +∞ (whereas for the annealed theorem, the optimal condition is E (τ12) < +∞

A quenched functional central limit theorem for random walks in random environments under (T)γ

We prove a quenched central limit theorem for random walks in i.i.d. weakly elliptic random environments in the ballistic regime. Such theorems have been proved recently under the assumption of large finite moments for the regeneration times. In this paper, we relax these moment assumptions under Sznitman's (T)γ ballisticity condition, which allows the inclusion of new non-uniformly elliptic examples such as Dirichlet random environments

Iron metabolism imbalance at the time of listing increases overall and infectious mortality after liver transplantation

International audienceBACKGROUND Liver transplantation (LT) is the best treatment for patients with liver cancer or end stage cirrhosis, but it is still associated with a significant mortality. Therefore identifying factors associated with mortality could help improve patient management. The impact of iron metabolism, which could be a relevant therapeutic target, yield discrepant results in this setting. Previous studies suggest that increased serum ferritin is associated with higher mortality. Surprisingly iron deficiency which is a well described risk factor in critically ill patients has not been considered. AIM To assess the impact of pre-transplant iron metabolism parameters on post-transplant survival. METHODS From 2001 to 2011, 553 patients who underwent LT with iron metabolism parameters available at LT evaluation were included. Data were prospectively recorded at the time of evaluation and at the time of LT regarding donor and recipient. Serum ferritin (SF) and transferrin saturation (TS) were studied as continuous and categorical variable. Cox regression analysis was used to determine mortality risks factors. Follow-up data were obtained from the local and national database regarding causes of death. RESULTS At the end of a 95-mo median follow-up, 196 patients were dead, 38 of them because of infections. In multivariate analysis, overall mortality was significantly associated with TS &gt; 75% [HR 1.73 (1.14; 2.63)], SF &lt; 100 mu g/L [HR 1.62 (1.12; 2.35)], hepatocellular carcinoma [HR 1.58 (1.15; 2.26)], estimated glomerular filtration rate (CKD EPI Cystatin C) [HR 0.99 (0.98; 0.99)], and packed red blood cell transfusion [HR 1.05 (1.03; 1.08)]. Kaplan Meier curves show that patients with low SF (&lt; 100 mu g/L) or high SF (&gt; 400 mu g/L) have lower survival rates at 36 mo than patients with normal SF (P = 0.008 and P = 0.016 respectively). Patients with TS higher than 75% had higher mortality at 12 mo (91.4% +/- 1.4% vs 84.6% +/- 3.1%, P = 0.039). TS &gt; 75% was significantly associated with infection related death [HR 3.06 (1.13; 8.23)]. CONCLUSION Our results show that iron metabolism imbalance (either deficiency or overload) is associated with post-transplant overall and infectious mortality. Impact of iron supplementation or depletion should be assessed in prospective study