Mathematics

In this paper, we give a short Bayesian proof of Talagrand's celebrated majorizing-measure theorem (MMT). While the upper-bound direction of MMT follows relatively directly from standard arguments, the lower-bound direction is widely…

We study Bernoulli percolation on $\mathbb Z^d$ in dimensions ${d>6}$. We prove that a classical consequence of the van den Berg-Kesten inequality, often referred to as the Simon-Lieb inequality in the context of the Ising model, admits a…

We study the moduli stacks of real vector bundles of fixed rank and degree on a type I real algebraic curve and determine its mod 2 cohomology algebra in terms of characteristic classes.

The crystalline differential operators on a smooth variety X give rise to a non-split Azumaya algebra over the cotangent bundle of the Frobenius twist X'. In some cases, this Azumaya algebra splits when restricted to finite covers of X'. In…

We prove an inversion theorem for recursive formulas satisfied by certain families of converging power series in two variables. These power series are indexed by the Harder-Narasimhan types of principal $G$-bundles of degree $d \in \pi_1 G$…

The renewal contact process is a non-Markovian variant of the classical contact process in which recoveries are governed by independent renewal processes with interarrival distribution $\mu$. We establish new sufficient conditions ensuring…

In this note, we give short proofs of three theorems concerning extremal problems in the Johnson scheme, or, in other terminology, on $(n,k,L)$-systems. The main result is a proof of the Aljohani--Bamberg--Cameron conjecture which claims…

We derive closed form expressions for the lower expectations that correspond to total variation distance and chi-squared divergence balls around a probability mass function over a finite set.

We investigate integration by parts (IBP) formulae for stochastic Volterra equations and we establish the smoothing effect of the expectation. Due to the inherent path-dependent dynamics of this class of processes, standard…

We show that any big line bundle on a smooth projective variety admits a special Fujita approximation: the volume and the first Riemann-Roch coefficient are both approximated by those of ample $\mathbb{Q}$-line bundles on higher models.…

Importance sampling (IS) consists in biasing samples from a distribution $f$ towards another distribution $g$. Concretely, given samples $X_i$ from $f$, the IS measure is $$\hat{g}_n = \frac{1}{Z_n}\sum_{i=1}^n \frac{g(X_i)}{f(X_i)}…

Using the Baxter-Kelland-Wu coupling and the convergence of the height function of the six-vertex model to the Gaussian Free Field, we extract critical exponents for the planar critical random-cluster model at $q=4$, and the planar…

We use the machinery of a conditional probability space (R\'enyi, 1955) to obtain an Agreement Theorem (Aumann, 1976) under general conditions. A conditional probability space (CPS) is a family of probability measures defined relative to a…

All reduced descendent Gromov-Witten invariants of $K3$ and abelian surfaces in primitive curve classes can be calculated by the methods of \cite{BOPY,MPT}. To handle the imprimitive curve classes, a multiple cover formula was conjectured…

We consider $N\times N$ matrices $X$ with independent, identically distributed entries, and prove that the sequence of measures $\frac{ | \det (X-z)|^\gamma}{\mathbb{E}[ | \det (X-z)|^\gamma]}$ converge to the Gaussian Multiplicative Chaos…

Let $X$ be a proper smooth rigid analytic variety over a complete algebraically closed field $p$-adic field $\mathbf C$. Fix an continuation $\mathrm{Exp}$. Faltings (in the curve case) and Heuer showed that any lifting $\widetilde X$ of…

We extend the notion of mex, which is central in combinatorial number theory, to an arbitrary combinatorial structure, and we prove a general theorem to determine the generating function of the objects having fixed mex. We then study this…

We consider Subtraction Nim, where two players have exactly the same options, but which is partizan in the sense that at the game ending, a partizan rule is applied for the decision of the winner. We consider the following example: Let $S$…

We study a question of Harju from 2019 regarding the existence of infinite ternary square-free words whose subsequences modulo $p$ and $q$ are also square-free for relatively prime integers $p$ and $q$. Among such pairs $(p, q)$ with $p, q…

We introduce variants of the Maker-Breaker and Waiter-Client games, which we call \emph{stotting}, in which a player grants a slight advantage to the opponent. We prove that a winning strategy in either stotting variant yields winning…