Research
Research
Research
Research
2,313+ open-access research outputs.
We construct the multilevel correlation kernel for the rising GUE eigenvalue process starting from a fixed initial configuration $x^{(m)}$, and show that it converges on short time scales (as quickly …
We address the question of the large-time behavior of solutions to reaction-diffusion equations in periodic media. We start with the description of the asymptotic shape of the invasion set, which is c…
We show that the loop homology algebras of polyhedral products of the form $(\underline{X},\underline{*})^{\mathcal{K}}$ can be written as a colimit over the flagification of $\mathcal{K}$, and obtain…
We construct a family of velocity fields demonstrating the sharpness of the classical Zvonkin--Veretennikov--Davie strong well-posedness by noise regime. We consider stochastic differential equations …
In this paper, we obtain a weighted trigonometric summation formula which is an extension of the trigonometric summation formula by Grigor'yan, Lin and Yau \cite{GLY}.…
We consider the compressible Euler system for ideal gas flow in the absence of any forces except the internal thermodynamic pressure. In this setting, and in dimensions higher 1, it is known that …
Unconditional guaranteed lower and upper eigenvalue bounds are mandatory for the understanding of the Schr\"odinger eigenvalue spectrum and its spectral gaps. While upper eigenvalue bounds are natural…
Rex, short for Reverse Hex, is a set coloring game in which players try to avoid connecting terminals of their color. Combinatorial game theory (CGT) is the study of perfect strategy games. Until rece…
The first paper in this series introduced a \emph{short-to-long mixing} condition that captures mean-field GOE/GUE edge universality in the supercritical sparsity regime, for symmetric/Hermitian rando…
The extent to which the geometry of an object is determined by some associated spectral data is a longstanding problem. We investigate this problem in the context of the Steklov spectrum, focusing on …
We study the Weyl functional on connected sums of two four-dimensional manifolds $(M,g_M)$ and $(Z,g_Z)$, assuming $g_M$ is Bach-flat and $g_Z$ locally conformally flat. We show that if $g_M$ is neith…
We study a model of market economics wherein the $(n+1)$-st customer, for each $n\geqslant N$, with $N$ being a prespecified positive integer, draws a sample of (random) size $K_{n}$, either with repl…
We propose a method for the prediction of stationary max--stable random fields with $\alpha$-Fr\'echet marginal distribution $H_\alpha$. The method is suitable to cope with heavy tails for $\alpha\in(…
We develop a stochastic free-boundary model of housing tenure decisions in markets with high mobility risk, such as areas near military installations. Housing prices and rents follow correlated diffus…
We study $v_n$-periodic phenomena in $C_2$-equivariant stable homotopy through the lens of the $C_2$-equivariant Adams spectral sequence at the prime 2. In particular, we construct/detect certain clas…
We study topological rigidity of real moment-angle manifolds associated to flag simplicial complexes. Using the cubical geometry arising from the Davis construction, we identify the universal cover wi…
We study dimensions of sets projected to an $(n-2)$-dimensional family of hyperplanes in $\mathbb{R}^n$ under curvature conditions. Let $n\ge 3$ and $\Sigma \subset S^{n-1}$ be an $(n-2)$-dimensional …
Davis, Drusvyatskiy, and Jiang showed that gradient descent with an adaptive stepsize converges locally at a nearly-linear rate for smooth functions that grow at least quartically away from their mini…
In this paper we prove that if a closed set in R^N is close to a cone over a simplicial complex at each point and at each scale, then it is locally bi-H\"older equivalent to such a cone. This generali…
Given integers $p,q,t$ with $1 \le t \le p$ and $1 \le q \le h_p(t)$, a strong $(p,q,t)$-coloring of the Boolean lattice $B_n$ is a coloring of its $t$-chains such that every induced copy of $B_p$ in …
Free open-access publishing with Google Scholar indexing.
Submission Guide →