Related papers: The stability of log-supermodularity under convolu…

For perturbations of integrable Hamiltonians systems, the Nekhoroshev theorem shows that all solutions are stable for an exponentially long interval of time, provided the integrable part satisfies a steepness condition and the system is…

In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…

In this paper, we mainly study the stability of iterated polynomials and linear transformations preserving the strong $q$-log-convexity of polynomials Let $[T_{n,k}]_{n,k\geq0}$ be an array of nonnegative numbers. We give some criteria for…

We survey the symmetry preserving properties for the dual propinquity, under natural non-degeneracy and equicontinuity conditions. These properties are best formulated using the notion of the covariant propinquity when the symmetries are…

We study various regularization operators on plurisubharmonic functions that preserve Lelong classes with growth given by certain compact convex sets. The purpose is to show that the weighted Siciak-Zakharyuta functions associated with…

We present two results related to magnetized Vlasov equations. Our first contribution concerns the stability of solutions to the magnetized Vlasov-Poisson system with a non-uniform magnetic field using the optimal transport approach…

The paper presents methods of eigenvalue localisation of regular matrix polynomials, in particular, stability of matrix polynomials is investigated. For this aim a stronger notion of hyperstability is introduced and widely discussed. Matrix…

We prove, using optimal transport tools, weighted Poincar'e inequalities for log-concave random vectors satisfying some centering conditions. We recover by this way similar results by Klartag and Barthe-Cordero-Erausquin for log-concave…

Consider a family of modular forms of weight 2, all of whose residual $\pmod{p}$ Galois representations are isomorphic. It is well-known that their corresponding Iwasawa $\lambda$-invariants may vary. In this paper, we study this variation…

General extensions of an inequality due to Rogozin, concerning the essential supremum of a convolution of probability density functions on the real line, are obtained. While a weak version of the inequality is proved in the very general…

We propose a stability criterion of superfluids in condensed Bose-Einstein systems, which incorporates the spectral function or the autocorrelation function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory, we demonstrate…

The robust statistical description of dynamical systems under perturbations is a central problem in ergodic theory. In this paper, we investigate the statistical properties of skew-product maps driven by a subshift of finite type with…

In terms of a nice reference probability measure, integrability conditions on the path-dependent drift are presented for (infinite-dimensional) degenerate PDEs to have regular positive solutions. To this end, the corresponding stochastic…

We consider probability mass functions $V$ supported on the positive integers using arguments introduced by Caputo, Dai Pra and Posta, based on a Bakry--\'{E}mery condition for a Markov birth and death operator with invariant measure $V$.…

We consider the Arveson-Douglas conjecture on the essential normality of homogeneous submodules corresponding to algebraic subvarieties of the unit ball. We prove that the property of essential normality is preserved by isomorphisms between…

Let $\sigma_1$ and $\sigma_2$ be commuting involutions of a semisimple algebraic group $G$. This yields a $Z_2\times Z_2$-grading of $\g=\Lie(G)$, $\g=\bigoplus_{i,j=0,1}\g_{ij}$, and we study invariant-theoretic aspects of this…

In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…

We establish an improved form of the classical logarithmic Sobolev inequality for the Gaussian measure restricted to probability densities which satisfy a Poincar\'e inequality. The result implies a lower bound on the deficit in terms of…

By using optimal mass transport theory, we provide a direct proof to the sharp $L^p$-log-Sobolev inequality $(p\geq 1)$ involving a log-concave homogeneous weight on an open convex cone $E\subseteq \mathbb R^n$. The perk of this proof is…

This paper uses convolutions of the gamma density and the one-sided stable density to construct higher level densities. The approach is applied to constructing a 4-parameter Mittag-Leffler density, whose Laplace transform is a corresponding…