Related papers: An Invariance Principle for the Multi-slice, with …
This paper establishes a sharp Schwarz-Pick type inequality for real-valued invariant harmonic functions defined on the complex unit ball $\mathbb B^n$. The proof of this main result simultaneously provides a solution to a natural extension…
I provide a proof of the existence of absolutely continuous invariant measures (and study their statistical properties) for multidimensional piecewise expanding systems with not necessarily bounded derivative or distortion. The proof uses…
We obtain a strong invariance principle for nonconventional sums and applying this result we derive for them a version of the law of iterated logarithm, as well as an almost sure central limit theorem. Among motivations for such results are…
We continue the study of the covering complexity of constraint satisfaction problems (CSPs) initiated by Guruswami, H{\aa}stad and Sudan [SIAM J. Comp. 2002] and Dinur and Kol [CCC'13]. The covering number of a CSP instance $\Phi$ is the…
Uncertainty estimation in deep models is essential in many real-world applications and has benefited from developments over the last several years. Recent evidence suggests that existing solutions dependent on simple Gaussian formulations…
We advance scale-invariance arguments for systems that are governed (or approximated) by a $q-$Gaussian distribution, i.e., a power law distribution with exponent $Q=1/(1-q); q \in \mathbb{R}$. The ensuing line of reasoning is then compared…
In this work, we address the problem of approximating the $k$-disc distribution ("frequency vector") of a bounded-degree graph in sublinear-time under the assumption of hyperfiniteness. We revisit the partition-oracle framework of Hassidim,…
We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up…
A vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ of $G$ is called a \emph{transitive partition} of size $k$ if $V_i$ dominates $V_j$ for all $1\leq i<j\leq k$. For two disjoint subsets $A$ and $B$ of $V$, we say $A$ \emph{strongly…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
We consider combining the definition of a cardinal invariant and the notion of an infinite game. We focus on the splitting number $\mathfrak{s}$ since the corresponding cardinal invariants behave in an interesting way. We introduce three…
A \emph{multipacking} in an undirected graph $G=(V,E)$ is a set $M\subseteq V$ such that for every vertex $v\in V$ and for every integer $r\geq 1$, the ball of radius $ r $ around $ v $ contains at most $r$ vertices of $M$. The…
Stochastic dominance (SD) provides a quantile-based partial ordering of random variables and has broad applications. Its extension to multivariate settings, however, is challenging due to the lack of a canonical ordering in $\mathbb{R}^d$…
As the size of engineered systems grows, problems in reliability theory can become computationally challenging, often due to the combinatorial growth in the cut sets. In this paper we demonstrate how Multilevel Monte Carlo (MLMC) - a…
When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…
A value of a CSP instance is typically defined as a fraction of constraints that can be simultaneously met. We propose an alternative definition of a value of an instance and show that, for purely combinatorial reasons, a value of an…
We exhibit a class of "relatively curved" $\vec{\gamma}(t) := (\gamma_1(t),\dots,\gamma_n(t))$, so that the pertaining multi-linear maximal function satisfies the sharp range of H\"{o}lder exponents, \[ \left\| \sup_{r > 0} \ \frac{1}{r}…
Based on results by Brugall\'e and Mikhalkin, Fomin and Mikhalkin give formulas for computing classical Severi degrees $N^{d, \delta}$ using long-edge graphs. In 2012, Block, Colley and Kennedy considered the logarithmic version of a…
We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…