Related papers: The convex hull for a random acceleration process …

We relate the expected hyperbolic length of the perimeter of the convex hull of the trajectory of Brownian motion in the hyperbolic plane to an expectation of a certain exponential functional of a one-dimensional real-valued Brownian…

Kernel quadrature can exploit RKHS spectral structure and outperform Monte Carlo on smooth integrands, but optimized quadrature weights are generally signed and may be numerically unstable. We study whether spectral acceleration remains…

This paper develops a unified framework for estimating the volume of a set in $\mathbb{R}^d$ based on observations of points uniformly distributed over the set. The framework applies to all classes of sets satisfying one simple axiom: a…

We study extremal properties of spherical random polytopes, the convex hull of random points chosen from the unit Euclidean sphere in $\mathbb{R}^n$. The extremal properties of interest are the expected values of the maximum and minimum…

It is well known that for a standard Brownian motion (BM) $ \{B(t), \;t \geq 0\}$ with values in $\mathbb{R}^d$, its convex hull $ V(t)=\conv \{\{\,B(s),\;s \leq t \}$ with probability $1$ for each $t > 0$ contains $0$ as an interior point…

N. Dolbilin and M. Tanemura studied the convex hulls of finite subsets of the Clifford torus $T$ in $E^4$. They have completely studied the combinatorial structure of the convex hull for a periodic point set. Moreover, there was performed a…

Motivated by previous efforts toward mathematically analyzing the treatment of monomials in spatial branch-and-bound, we study the convex hull of the graph of a simple monomial on a nonnegative box domain in arbitrary dimension, where at…

We study the random acceleration model, which is perhaps one of the simplest, yet nontrivial, non-Markov stochastic processes, and is key to many applications. For this non-Markov process, we present exact analytical results for the…

We consider the statistics of the areas enclosed by domain boundaries (`hulls') during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls…

We propose a new model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its…

In the focus of our attention is the asymptotic properties of the sequence of convex hulls which arise as a result of a peeling procedure applied to the convex hull generated by a Poisson point process. Processes of the considered type are…

Let $T$ be the triangle in the plane with vertices $(0, 0)$, $(0,1)$ and $(0, 1)$. The convex hull $T_n$ of points $(0, 1)$, $(1, 0)$ and $n$ independent random points uniformly distributed in $T$ is the random convex chain. In this paper…

In this work we deal with the problem of support estimation under shape restrictions. The shape restriction we deal with is an extension of the notion of convexity named alpha-convexity. Instead of assuming, as in the convex case, the…

We develop polynomial-time algorithms for near-optimal minimax mean estimation under $\ell_2$-squared loss in a Gaussian sequence model under convex constraints. The parameter space is an origin-symmetric, type-2 convex body $K \subset…

The convex hull of a data set $P$ is the smallest convex set that contains $P$. In this work, we present a new data structure for convex hull, that allows for efficient dynamic updates. In a dynamic convex hull implementation, the following…

Writing an uncomplicated, robust, and scalable three-dimensional convex hull algorithm is challenging and problematic. This includes, coplanar and collinear issues, numerical accuracy, performance, and complexity trade-offs. While there are…

Let $P$ be a set of $n$ points in $\mathbb{R}^3$ in general position, and let $RCH(P)$ be the rectilinear convex hull of $P$. In this paper we obtain an optimal $O(n\log n)$-time and $O(n)$-space algorithm to compute $RCH(P)$. We also…

We study the convex hulls of reachable sets of nonlinear systems with bounded disturbances and uncertain initial conditions. Reachable sets play a critical role in control, but remain notoriously challenging to compute, and existing…

We prove large deviations principles (LDPs) for the perimeter and the area of the convex hull of a planar random walk with finite Laplace transform of its increments. We give explicit upper and lower bounds for the rate function of the…

We compute the lamination convex hull of the stationary IPM equations. We also show in bounded domains that for subsolutions of stationary IPM taking values in the lamination convex hull, velocity vanishes identically and density depends…