Related papers: Sharp supremum and H\"older bounds for stochastic …
We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier's power functions bounds $t^p$, with $p \geq 2$, and they are related to the notion…
Sturm's strong law of large numbers in $\mathrm{CAT}(0)$ spaces has been an influential tool to study the geometric mean or also called Karcher barycenter of positive definite matrices. It provides an easily computable stochastic…
Recently a majorization method for optimizing partition functions of log-linear models was proposed alongside a novel quadratic variational upper-bound. In the batch setting, it outperformed state-of-the-art first- and second-order…
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in…
We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…
This paper analyzes the Lipschitz behavior of the feasible set in two parametric settings, associated with linear and convex systems in R^n. To start with, we deal with the parameter space of linear (finite/semi-infinite) systems identified…
We consider a semigroup of operators in the Banach space $C_b(H)$ of uniformly continuous and bounded functions on a separable Hilbert space $H$. In particular, we deal with semigroups that are related to solution of stochastic PDEs in $H$…
Supersymmetric domain-wall spacetimes that lift to Ricci-flat solutions of M-theory admit generalized Heisenberg (2-step nilpotent) isometry groups. These metrics may be obtained from known cohomogeneity one metrics of special holonomy by…
We derive a stochastic Gronwall lemma with suprema over the paths in the upper bound of the assumed affine-linear growth assumption. This allows applications to It\^o processes with coefficients which depend on earlier time points such as…
The purpose of this investigation is to extend basic equations and inequalities which hold for functions $f$ in a Bernstein space $B_\sigma^2$ to larger spaces by adding a remainder term which involves the distance of $f$ from $B_\sigma^2$.…
The invariant integration method for Chern-Simons theory for gauge group SU(2) and manifold \Gamma\H^3 is verified in the semiclassical approximation. The semiclassical limit for the partition function associated with a connected sum of…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
We study boundary inference at $H=3/4$ for mixed fractional Brownian motion and mixed fractional Ornstein--Uhlenbeck models under high-frequency observation. This boundary is economically important because it separates the critical and…
P. Buser and P. Sarnak showed in 1994 that the maximum, over the moduli space of Riemann surfaces of genus s, of the least conformal length of a nonseparating loop, is logarithmic in s. We present an application of (polynomially) dense…
High-dimensional planted problems, such as finding a hidden dense subgraph within a random graph, often exhibit a gap between statistical and computational feasibility. While recovering the hidden structure may be statistically possible, it…
Based on the recently introduced uniform $\lambda-$adjustment for closed subspaces of Banach spaces we extend the concept of the strictly singular and finitely strictly singular operators to the sequences of closed subspaces and operators…
Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane. When the integrand is of rapid decay near the cusps, the integral can be computed by the…
We prove a transference principle for general (i.e., not necessarily bounded) strongly continuous groups on Banach spaces. If the Banach space has the UMD property, the transference principle leads to estimates for the functional calculus…
In this article we prove that for any orthonormal system $(\vphi_j)_{j=1}^n \subset L_2$ that is bounded in $L_{\infty}$, and any $1 < k <n$, there exists a subset $I$ of cardinality greater than $n-k$ such that on $\spa\{\vphi_i\}_{i \in…
In this paper, we first study the existence-uniqueness and large deviation estimate of solutions for stochastic Volterra integral equations with singular kernels in 2-smooth Banach spaces. Then, we apply them to a large class of semilinear…