Related papers: Counterexamples to Okounkov's Log-Concavity Conjec…

We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the…

We discuss several counterexamples to a rigidity conjecture of K. Khanin, which states that under some quantitative condition on non-existence of periodic orbits, $C^0$ conjugacy implies $C^1$ (even $C^\infty$) conjugacy. We construct…

We prove that the Laptev--Safronov conjecture (Comm. Math. Phys., 2009) is false in the range that is not covered by Frank's positive result (Bull. Lond. Math. Soc., 2011). The simple counterexample is adaptable to a large class of…

We prove sharp anti-concentration results for log-concave random variables on the real line in both the discrete and continuous setting. Our approach is elementary and uses majorization techniques to recover and extend some recent and not…

In this note, we disprove two Romanov type conjectures posed by Chen.

Let $Q_n(z)$ be the polynomials associated with the Nekrasov-Okounkov formula $$\sum_{n\geq 1} Q_n(z) q^n := \prod_{m = 1}^\infty (1 - q^m)^{-z - 1}.$$ In this paper we partially answer a conjecture of Heim and Neuhauser, which asks if…

We prove several congruences for trinomial coefficients.

We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of Knutson-Tao-Woodward on the facets of the…

In this paper we use computational methods to disprove a conjecture by Alaoglu and Erd\H{o}s regarding the superabundant numbers.

The asymptotic variety of a counterexample of Pinchuk type to the strong real Jacobian conjecture is explicitly described by low degree polynomials.

We build here several counterexamples for two weight bi-parameter Carleson embedding theorem.

We prove some new equivalences of the paving conjecture and obtain some estimates on the paving constants. In addition we give a new family of counterexamples to one of the Akemann-Anderson conjectures.

We consider the problem of causal inference based on observational data (or the related missing data problem) with a binary or discrete treatment variable. In that context, we study inference for the counterfactual density functions and…

We prove that the (B) conjecture and the Gardner-Zvavitch conjecture are true for all log-concave measures that are rotationally invariant, extending previous results known for Gaussian measures. Actually, our result apply beyond the case…

By the Pr\'ekopa-Leindler inequality, the difference $X-X'$ has a log-concave density provided that $X$ has a log-concave density and $X, X'$ are independent and identically distributed. We prove that the opposite direction does not always…

We will prove a reverse Rogers-Shephard inequality for log-concave functions. In some particular cases, the method used for general log-concave functions can be slightly improved, allowing us to prove volume estimates for polars of…

We present a counterexample to Conjecture~14.1.6 from [Vladimir Kanovei, Borel equivalence relations], regarding Borel equivalence relations on product spaces.

Firstly, we propose our conjectured Reverse-log-Brunn-Minkowski inequality (RLBM). Secondly, we show that the (RLBM) conjecture is equivalent to the log-Brunn-Minkowski (LBM) conjecture proposed by B\"or\"oczky-Lutwak-Yang-Zhang. We name…

A conjecture of Woods from 1972 is disproved.

We propose a variant of the effective adjunction conjecture for lc-trivial fibrations. This variant is suitable for inductions and can be used to treat real coefficients.