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Dans cet article, nous pénalisons la loi d’une araignée brownienne ${\left(A_t\right)}_{t\ge 0}$ prenant ses valeurs dans un ensemble fini $E$ de demi-droites concourantes, avec un poids égal à $\frac{1}{Z_t}exp({\alpha }_{N_t}{X}_t+\gamma L_t)$, où $t$ est un réel positif, ${\left({\alpha }_k\right)}_{k\in E}$ une famille de réels indexés par $E$, $\gamma$ un paramètre réel, $X_t$ la distance de $A_t$ à l’origine, $N_t$ ($\in E$) la demi-droite sur laquelle se trouve $A_t$, $L_t$ le temps local de ${\left(X_s\right)}_{0\le s\le t}$ à l’origine, et $Z_t$ la constante de normalisation. Nous montrons que la famille des mesures de probabilité obtenue par ces pénalisations converge vers...

Let (Ω, $ℱ$, (${ℱ}_t$), $\mathbb{P}$) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ${ℱ}_{\infty }$ (the-algebra generated by (${ℱ}_t$)) a coherent family of probability measures (${\mathbb{Q}}_t$) indexed by , each of them being defined on ${ℱ}_t$. It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer if...

In this article we study in detail a family of random matrix ensembles which are obtained from random permutations matrices (chosen at random according to the Ewens measure of parameter $\theta \>0$) by replacing the entries equal to one by more general non-vanishing complex random variables. For these ensembles, in contrast with more classical models as the Gaussian Unitary Ensemble, or the Circular Unitary Ensemble, the eigenvalues can be very explicitly computed by using the cycle structure of the permutations....

Let (Ω, $ℱ$, (${ℱ}_t$), $\mathbb{P}$) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to ${ℱ}_{\infty }$ (the -algebra generated by (${ℱ}_t$)) a coherent family of probability measures (${\mathbb{Q}}_t$) indexed by , each of them being defined on ${ℱ}_t$. It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative answer...