Tuan Tran, Anti-concentration phenomena
Let $X$ be a real random variable; a typical anti-concentration inequality asserts that (under certain assumptions) if an interval $I$ has small length, then $\mathbb{P}(X\in I)$ is small, regardless the …
Let $X$ be a real random variable; a typical anti-concentration inequality asserts that (under certain assumptions) if an interval $I$ has small length, then $\mathbb{P}(X\in I)$ is small, regardless the …
In the early 1980s, Beck proved that, if P is a set of n points in the real plane, and no more than g points of P lie on any …
I give a quick survey on stability and NIP(Non-Independent Property). We first review basic facts on the first order logic and give some historical remarks on classification theory in model theory. …
I give a quick survey on stability and NIP(Non-Independent Property). We first review basic facts on the first order logic and give some historical remarks on classification theory in model theory. …
I give a quick survey on stability and NIP(Non-Independent Property). We first review basic facts on the first order logic and give some historical remarks on classification theory in model theory. …
Let E be a finite set and I be a collection of subsets of E. When is there a set of real vectors indexed by E such that I correspond to its linearly independent subsets? In 1935, …
Generalized extremal problems have been one of the central topics of study in extremal combinatorics throughout the last few decades. One such simple-looking problem, maximizing the number of cliques of …
Let $G$ be a graph on the vertex set $V$. A vertex subset $W \subset V$ is a cover of $G$ if $V \setminus W$ is an independent set of …
Let $G$ be a graph on $V$ and $n$ a positive integer. Let $I_n(G)$ be the abstract simplicial complex whose faces are the subsets of $V$ that do not contain …
For any given graph $H$, one may define a natural corresponding functional $\|.\|_H$ for real-valued functions by using homomorphism density. One may also extend this to complex-valued functions, once $H$ …