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pro vyhledávání: '"Louis, Pierre"'
We consider a system of diffusion processes interacting through their empirical distribution. Assuming that the empirical average of a given observable can be observed at any time, we derive regularity and quantitative stability results for the optim
Externí odkaz:
http://arxiv.org/abs/2410.23016
We extend the Gibbs conditioning principle to an abstract setting combining infinitely many linear equality constraints and non-linear inequality constraints, which need not be convex. A conditional large large deviation principle (LDP) is proved in
Externí odkaz:
http://arxiv.org/abs/2410.20858
Autor:
Chaintron, Louis-Pierre
A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit theorem are proved for the empirical measure of a mean-field system of interacting diffusions. The coefficients are path-dependent. The framework allows for
Externí odkaz:
http://arxiv.org/abs/2410.04935
We prove a result on the large deviations of the central values of even primitive Dirichlet $L$-functions with a given modulus. For $V\sim \alpha\log\log q$ with $0<\alpha<1$, we show that \begin{equation}\nonumber\frac{1}{\varphi(q)} \# \left\{\chi
Externí odkaz:
http://arxiv.org/abs/2405.20888
Autor:
Arguin, Louis-Pierre, Hamdan, Jad
We derive precise upper bounds for the maximum of the Riemann zeta function on short intervals on the critical line, showing for any $\theta\in(-1,0]$, the set of $t\in [T,2T]$ for which $$\max_{|h|\leq \log^\theta T}|\zeta(\tfrac{1}{2}+it+ih)|>\exp\
Externí odkaz:
http://arxiv.org/abs/2405.06474
Autor:
Arguin, Louis-Pierre, Bailey, Emma
Let $\delta>0$ and $\sigma=\frac{1}{2}+\tfrac{\delta}{\log T}$. We prove that, for any $\alpha>0$ and $V\sim \alpha\log \log T$ as $T\to\infty$, $\frac{1}{T}\text{meas}\big\{t\in [T,2T]: \log|\zeta(\sigma+\rm{i} \tau)|>V\big\}\geq C_\alpha(\delta)\in
Externí odkaz:
http://arxiv.org/abs/2403.19803
Autor:
Chaintron, Louis-Pierre
The purpose of this article is to prove existence, uniqueness and uniform gradient estimates for unbounded classical solutions of a Hamilton-Jacobi-Bellman equation. Such an equation naturally arises in stochastic control problems. Contrary to the cl
Externí odkaz:
http://arxiv.org/abs/2309.11813
We prove a lower bound on the maximum of the Riemann zeta function in a typical short interval on the critical line. Together with the upper bound from the previous work of the authors, this implies tightness of $$ \max_{|h|\leq 1}|\zeta(\tfrac 12+{\
Externí odkaz:
http://arxiv.org/abs/2307.00982