相关论文: Border Waring Rank via Asymptotic Rank

We study the relationship between the commutative and the non-commutative rank of a linear matrix. We give examples that show that the ratio of the two ranks comes arbitrarily close to 2. Such examples can be used for giving lower bounds…

In this paper the asymptotic distribution of estimators is derived in a general regression setting where rank restrictions on a submatrix of the coefficient matrix are imposed and the regressors can include stationary or I(1) processes.…

We give a sufficient condition for the strong symmetric version of Strassen's additivity conjecture: the Waring rank of a sum of forms in independent variables is the sum of their ranks, and every Waring decomposition of the sum is a sum of…

We study path-connectedness and homotopy groups of sets of tensors defined by tensor rank, border rank, multilinear rank, as well as their symmetric counterparts for symmetric tensors. We show that over $\mathbb{C}$, the set of rank-$r$…

We show that Haar measures of connected semisimple groups, embedded via a representation into a matrix space, have a homogeneous asymptotic limit when viewed from far away and appropriately rescaled. This is still true if the Haar measure…

We prove the meridional rank conjecture for twisted links and arborescent links associated to bipartite trees with even weights. These links are substantial generalizations of pretzels and two-bridge links, respectively. Lower bounds on…

For tensors of fixed order, we establish three types of upper bounds for the geometric rank in terms of the subrank. Firstly, we prove that, under a mild condition on the characteristic of the base field, the geometric rank of a tensor is…

We establish the vanishing for non-trivial unitary representations of the bounded cohomology of SL_d up to the rank. It holds more generally for uniformly bounded representations on superreflexive spaces. The same results are obtained for…

Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…

We give a short proof of the convergence to the boundary of Riemann maps on varying domains. Our proof provides a uniform approach to several ad-hoc constructions that have recently appeared in the literature.

Asymptotic expansion is constructed and justified for the solution to a nonuniform Neumann boundary-value problem for the Poisson equation with the right-hand side that depends both on longitudinal and transversal variables in a thin…

In this paper we introduce a new method to produce lower bounds for the Waring rank of symmetric tensors. We also introduce the notion of $e$-computability and we use it to prove that Strassen's Conjecture holds in infinitely many new…

We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number…

Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…

Establishing the limiting distribution of Chatterjee's rank correlation for a general, possibly non-independent, pair of random variables has been eagerly awaited by many. This paper shows that (a) Chatterjee's rank correlation is…

The nonnegative and positive semidefinite (PSD-) ranks are closely connected to the nonnegative and positive semidefinite extension complexities of a polytope, which are the minimal dimensions of linear and SDP programs which represent this…

Downarowicz and Maass (2008) have shown that every Cantor minimal homeomorphism with finite topological rank $K > 1$ is expansive. Bezuglyi, Kwiatkowski and Medynets (2009) extended the result to non-minimal cases. On the other hand,…

The results of Strassen and Raz show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we…

We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…

(EN) We revise the famous algorithm for symmetric tensor decomposition due to Brachat, Comon, Mourrain and Tsidgaridas. Afterwards, we generalize it in order to detect possibly different decompositions involving points on the tangential…