相关论文: Distribution of boundary points of expansion and a…

We show that the shifted Lonely Runner Conjecture (sLRC) holds for 5 runners. We also determine that there are exactly 3 primitive tight instances of the conjecture, only two of which are tight for the non-shifted conjecture (LRC). Our…

We investigate the statistics of encounters of a diffusing particle with different subsets of the boundary of a confining domain. The encounters with each subset are characterized by the boundary local time on that subset. We extend a…

Consider $n$ runners running on a circular track of unit length with constant speeds such that $k$ of the speeds are distinct. We show that, at some time, there will exist a sector $S$ which contains at least $|S|n+ \Omega(\sqrt{k})$…

One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the mutual ditribution P(\rho,\psi) of the…

Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…

The scaled standard Wigner matrix (symmetric with mean zero, variance one i.i.d. entries), and its limiting eigenvalue distribution, namely the semi-circular distribution, has attracted much attention. The $2k$th moment of the limit equals…

We are concerned with the computational problem of determining the covering radius of a rational polytope. This parameter is defined as the minimal dilation factor that is needed for the lattice translates of the correspondingly dilated…

We investigate the extreme value statistics of a one-dimensional Brownian motion (with the diffusion constant $D$) during a time interval $\left[0, t \right]$ in the presence of a reflective boundary at the origin, starting from a positive…

In this paper, we are interested in the issues on existence, uniqueness, and multiplicity of stationary distributions for McKean-Vlasov SDEs with jumps. In detail, with regarding to McKean-Vlasov SDEs driven by pure jump L\'{e}vy processes,…

Random walks on regular bounded degree expander graphs have numerous applications. A key property of these walks is that they converge rapidly to the uniform distribution on the vertices. The recent study of expansion of high dimensional…

Given natural parameters s and r, where $2\leq s\leq r$, we consider the distribution of a random variable $\xi=\sum\limits_{k=1}^{\infty}s^{-k}\xi_k\equiv\Delta^{r_s}_{\xi_1\xi_2...\xi_k...},$ where $(\xi_k)$ is a sequence of independent…

We derive a local limit theorem for normal, moderate, and large deviations for symmetric simple random walk on the square lattice in dimensions one and two that is an improvement of existing results for points that are particularly distant…

We shift the perspective on the interval fragmentation problem from division points to division spacings. This leads to a proof that is both simpler and stronger, establishing limiting distributions for partition points and spacings and,…

We continue the study of $\delta$-dispersion, a continuous facility location problem on a graph where all edges have unit length and where the facilities may also be positioned in the interior of the edges. The goal is to position as many…

In the binary hypothesis testing problem, it is well known that sequentiality in taking samples eradicates the trade-off between two error exponents, yet implementing the optimal test requires the knowledge of the underlying distributions,…

In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupling methods in order to identify the spectral gap in the case…

We establish an equidistribution result for push-forwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an application of our analysis we obtain new results regarding the…

For any recurrent random walk (S_n)_{n>0} on R, there are increasing sequences (g_n)_{n>0} converging to infinity for which (g_n S_n)_{n>0} has at least one finite accumulation point. For one class of random walks, we give a criterion on…

We consider the best-choice problem for independent (not necessarily iid) observations $X_1, \cdots, X_n$ with the aim of selecting the sample minimum. We show that in this full generality the monotone case of optimal stopping holds and the…

Distribution testing is a fundamental statistical task with many applications, but we are interested in a variety of problems where systematic mislabelings of the sample prevent us from applying the existing theory. To apply distribution…