Related papers: Self-intersection local time: Critical exponent, l…
Let us consider a solution of the time-inhomogeneous stochastic differential equation driven by a Brownian motion with drift coefficient $b(t,x)=\rho\,{\rm sgn}(x)|x|^\alpha/t^\beta$. This process can be viewed as a distorted Brownian…
In this paper we consider examples of positive generalized Wiener functions and we establish a large deviation principle for the generalized multiple intersection local time of the multidimensional Brownian motion.
We consider the inhomogeneous biharmonic nonlinear Schr\"odinger (IBNLS) equation in $\mathbb{R}^N$, $$i \partial_t u +\Delta^2 u -|x|^{-b} |u|^{2\sigma}u = 0,$$ where $\sigma>0$ and $b>0$. We first study the local well-posedness in $\dot…
We define a new diffusive matrix model converging towards the $\beta$-Dyson Brownian motion for all $\beta\in [0,2]$ that provides an explicit construction of $\beta$-ensembles of random matrices that is invariant under the…
We consider a family of Gagliardo-Nirenberg-Sobolev interpolation inequalities which interpolate between Sobolev's inequality and the logarithmic Sobolev inequality, with optimal constants. The difference of the two terms in the…
In this paper, we establish some general forms of the law of the iterated logarithm for independent random variables in a sub-linear expectation space, where the random variables are not necessarily identically distributed. Exponential…
We prove that the occupation measures of Brownian motions conditioned to have large intersections converge weakly, up to spatial shifts, to the measure whose density is the square of an optimizer of the Gagliardo-Nirenberg inequality. We do…
The population $\mathrm{KL}_{\inf}$ is a fundamental quantity that appears in lower bounds for (asymptotically) optimal regret of pure-exploration stochastic bandit algorithms, and optimal stopping time of sequential tests. Motivated by…
In this article, we study the family of probability measures (indexed by a positive real number t), obtained by penalization of the Brownian motion by a given functional of its local times at time t. We prove that this family tends to a…
We prove that there are arbitrarily large values of $t$ such that $|\zeta(1+it)| \geq e^{\gamma} (\log_2 t + \log_3 t) + \mathcal{O}(1)$. This essentially matches the prediction for the optimal lower bound in a conjecture of Granville and…
Let $\{B(t), t \geq 0\}$ be a standard Brownian motion in $\mathbb{R}$. Let $T$ be the first return time to 0 after hitting 1, and $\{L(T,x), x \in \mathbb{R}\}$ be the local time process at time $T$ and level $x$. The distribution of…
In this paper we consider the winding number, $\theta(s)$, of planar Brownian motion and study asymptotic behavior of the process of the maximum time, the time when $\theta(s)$ attains the maximum in the interval $0\le s \le t$. We find the…
The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen and subsequently used by others to study the $L^2$ and $L^3$ moduli of continuity of Brownian local time. A version of the DSLT for fractional…
We study semi Lagrangian approximation schemes for Hamilton Jacobi Bellman equations arising from finite horizon optimal control problems. Classical error estimates for these schemes include the term $\frac{1}{\Delta t}$ which leads to…
We provide a sufficient condition for the bounded law of the iterated logarithms for strictly stationary random fields expressable as a functional of i.i.d. random fields when the summation is done on rectangles. The study is done via the…
We describe an experiment that has set new limits on the time reversal invariance violating D coefficient in neutron beta-decay. The emiT experiment measured the angular correlation J . p_e x p_p using an octagonal symmetry that optimizes…
We consider the problem of the exact computation of the marginal eigenvalue distributions in the Laguerre and Jacobi $\beta$ ensembles. In the case $\beta=1$ this is a question of long standing in the mathematical statistics literature. A…
Einstein's locality is invoked to derive a correlation inequality. In the case of ideal experiments, this inequality is equivalent to Bell's original inequality of 1965 which, as is well known, is violated by a maximum factor of 1.5. The…
We derive an upper bound for the mean of the supremum of the empirical process indexed by a class of functions that are known to have variance bounded by a small constant $\delta$. The bound is expressed in the uniform entropy integral of…
In this article we establish some estimates related to the Gaussian densities and to Hermite polynomials in order to obtain an almost sure estimate for each term of the It\^{o}-Wiener expansion of the self-intersection local times of the…