Related papers: Number rigidity in superhomogeneous random point f…

In this paper we show that the family P_d of probability distributions on R^d with log-concave densities satisfies a strong continuity condition. In particular, it turns out that weak convergence within this family entails (i) convergence…

The localization spectra of Lyapunov vectors in many-particle systems at low density exhibit a characteristic bending behavior. It is shown that this behavior is due to a restriction on the maximum number of the most localized Lyapunov…

Let $X_1, X_2,\ldots$ be random elements of the Skorokhod space $D(\mathbb{R})$ and $\xi_1, \xi_2, \ldots$ positive random variables such that the pairs $(X_1,\xi_1), (X_2,\xi_2),\ldots$ are independent and identically distributed. The…

We consider first-passage percolation on the $d$ dimensional cubic lattice for $d \geq 2$; that is, we assign independently to each edge $e$ a nonnegative random weight $t_e$ with a common distribution and consider the induced random graph…

Let $d\geq 3$ be a constant and let $F$ be a $d$-regular graph on $[n]$ with not too many symmetries. By the union bound, the probability threshold for the existence of a spanning subgraph in $G(n,p)$ isomorphic to $F$ is at least…

We analyze the behavior of an ensemble of inertial particles in a one-dimensional smooth Gaussian velocity field, in the limit of large inertia, but considering a finite correlation time for the random field. We derive in this limit a…

A partition $\mathcal{P}$ of $\mathbb{R}^d$ is called a $(k,\varepsilon)$-secluded partition if, for every $\vec{p} \in \mathbb{R}^d$, the ball $\overline{B}_{\infty}(\varepsilon, \vec{p})$ intersects at most $k$ members of $\mathcal{P}$. A…

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

Gauging of space translations for nonrelativistic point particles in one dimension leads to general coordinate transformations with fixed Newtonian time. The minimal gauge invariant extension of the particle velocity requires the…

The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic…

Partial rigidity is a quantitative notion of recurrence and provides a global obstruction which prevents the system from being strongly mixing. A dynamical system $(X, \mathcal{X}, \mu, T)$ is partially rigid if there is a constant $\delta…

We present a brief survey of fluctuations and large deviations of particle systems with subextensive growth of the variance. These are called hyperuniform (or superhomogeneous) systems. We then discuss the relation between hyperuniformity…

Let $p(n)$ be the number of all integer partitions of the positive integer $n$ and let $\lambda$ be a partition, selected uniformly at random from among all such $p(n)$ partitions. It is known that each partition $\lambda$ has a unique…

We study the stabilization time of two common types of influence propagation. In majority processes, nodes in a graph want to switch to the most frequent state in their neighborhood, while in minority processes, nodes want to switch to the…

We study translation-invariant additive equations of the form $\sum_{i=1}^s \lambda_i \mathbf{P}(\mathbf{n}_i) = 0$ in variables $\mathbf{n}_i \in \mathbb{Z}^d$, where the $\lambda_i$ are nonzero integers summing to zero, and $\mathbf{P}$…

We consider the probability that the random signed sum $\xi_1 v_1 + \dotsb + \xi_n v_n$ lies within a given distance $r$ of the origin, where $v_1,\dotsc,v_n \in \mathbb{R}^d$ are fixed unit vectors and $\xi_1,\dotsc,\xi_n$ are…

Given finite configurations $P_1, \dots, P_n \subset \mathbb{R}^d$, let us denote by $\mathbf{m}_{\mathbb{R}^d}(P_1, \dots, P_n)$ the maximum density a set $A \subseteq \mathbb{R}^d$ can have without containing congruent copies of any…

An infinite system of point particles placed in $\mathds{R}^d$ is studied. Its constituents perform random jumps with mutual repulsion described by a translation-invariant jump kernel and interaction potential, respectively. The pure states…

We present a uniform treatment of rigid supersymmetric field theories in a curved spacetime $\mathcal{M}$, focusing on four-dimensional theories with four supercharges. Our discussion is significantly simpler than earlier treatments,…

In limited data computerized tomography, the 2D or 3D problem can be reduced to a family of 1D problems using the differentiated backprojection (DBP) method. Each 1D problem consists of recovering a compactly supported function $f \in…