相关论文: Drums of high width
Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling…
In this note, we extend the scope of our previous work joint with Bonnafoux, Kattler, Ni\~no, Sedano-Mendoza, Valdez and Weitze-Schmith\"usen by showing the arithmeticity of the Kontsevich--Zorich monodromies of infinite families of…
We use the AdS/CFT correspondence to study flows of N=4 SYM to non-conformal theories. The dual geometries can be seen as sourced by a Wigner's semicircle distribution of D3 branes. We consider two cases, the first case corresponds to a…
Supersymmetric gauge theories in four dimensions have taught us many important physics lessons. These can both inform and be informed by future work on the lattice. I focus on three issues: the properties of supersymmetric Yang-Mills theory…
We derive exponential bounds on probabilities of large deviations for "light tail" martingales taking values in finite-dimensional normed spaces. Our primary emphasis is on the case where the bounds are dimension-independent or nearly so.…
We consider a class of stochastic growth models on the integer lattice which includes various interesting examples such as the number of open paths in oriented percolation and the binary contact path process. Under some mild assumptions, we…
We define and study multiplicative connections in the tangent bundle of a Lie groupoid. Multiplicative connections are linear connections satisfying an appropriate compatibility with the groupoid structure. Our definition is natural in the…
We construct a large class of Riemannian manifolds of arbitrary dimension with Riesz transform unbounded on $L^p(M)$ for all $p > 2$. This extends recent results for Vicsek manifolds, and in particular shows that fractal structure is not…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
We study the conflict-free chromatic number of hypergraphs derived from the family of facets of $d$-dimensional cyclic polytopes with $n$ vertices. While in odd dimensions $d$ the problem is easy, for even dimensions the problem becomes…
We prove a conjecture of Helfgott on the structure of sets of bounded tripling in bounded rank, which states the following. Let $A$ be a finite symmetric subset of $\mathrm{GL}_n(\mathbf{F})$ for any field $\mathbf{F}$ such that $|A^3| \leq…
The study of the graph diameter of polytopes is a classical open problem in polyhedral geometry and the theory of linear optimization. In this paper we continue the investigation initiated in [4] by introducing a vast hierarchy of…
We consider operators arising from regular Dirichlet forms with vanishing killing term. We give bounds for the bottom of the (essential) spectrum in terms of exponential volume growth with respect to an intrinsic metric. As special cases we…
In this paper, we study the growth of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where $P_j(z)$ are polynomials for…
Barret, Evans, and Francis conjectured that if $G$ is the straight linear 3-tree with $n$ vertices and $H$ is the straight linear 3-tree with $n+1$ vertices then \[\lim_{n\rightarrow \infty} r_{H} (1, n+1) - r_G(1,n) = \frac{1}{14},\] where…
We explicitly derive a complementary pair of four-dimensional M-theory brane-world models, linked by a five-dimensional bulk, each of which has a unique anomaly-free chiral spectrum. This is done via resolution of local consistency…
It has long been argued that the continuum limit of the 3D Ising model is equivalent to a string theory. Unfortunately, in the usual starting point for this equivalence -- a certain lattice theory of surfaces -- it is not at all obvious how…
A famous conjecture of Erd\H{o}s asserts that for $k\ge 3$, the maximum number of edges in an $n$-vertex $k$-uniform hypergraph without $s+1$ pairwise disjoint edges is $\max\{\binom{n}{k}-\binom{n-s}{k},\binom{sk+k-1}{k}\}$. This problem…
For hyperbolic surfaces with geodesic boundary, we study the orthosystole, i.e. the length of a shortest essential arc from the boundary to the boundary. We recover and extend work by Bavard completely characterizing the surfaces maximizing…
We give upper-bounds for the dimension of some linear systems. The theorem improves the differential Horace method introduced by Alexander-Hirschowitz, and was conjectured by Simpson. Possible applications are the calculus of the dimension…