Related papers: On the Stability of Geometric Extremes
Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new…
The stability of random variables can be generalized in any convex cone. In this case the principal results about the LePage representation and the domains of attraction are analogous but different to those well known for general Banach…
In classical probability theory, the convergence of empirical frequencies to theoretical probabilities: as captured by the Law of Large Numbers (LLN): is treated as axiomatic and emergent from statistical assumptions such as independence…
Conformally K\"{a}hler, Einstein-Maxwell metrics and $f$-extremal metrics are generalization of canonical metrics in K\"{a}hler geometry. We introduce uniform K-stability for toric K\"{a}hler manifolds, and show that uniform K-stability is…
Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
It seems to be generally accepted that apparently anomalous cosmological observations, such as accelerating expansion, etc., necessarily are inconsistent with standard general relativity and standard matter sources. Following the…
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of…
Stable laws can be tempered by modifying the L\'evy measure to cool the probability of large jumps. Tempered stable laws retain their signature power law behavior at infinity, and infinite divisibility. This paper develops random walk…
We study a stability property of probability laws with respect to small violations of algorithmic randomness. A sufficient condition of stability is presented in terms of Schnorr tests of algorithmic randomness. Most probability laws, like…
I argue that if a special science satisfies certain key assumptions that are familiar from physicalist accounts of the special sciences and from physics, then its causal regularities have an associated notion of entropy, and that this…
In the context of holomorphic families of ${\mathbb P}^k$ endomorphisms, we show that various notions of stability are equivalent. This allows us to both extend and simplify the architecture of the proof of certain results of [BBD]
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…
We conjecture that the exceptional set in Manin's Conjecture has an explicit geometric description. Our proposal includes the rational point contributions from any generically finite map with larger geometric invariants. We prove that this…
A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…
We provide simple and constructive proofs of Harris-type theorems on the existence and uniqueness of an equilibrium and the speed of equilibration of discrete-time and continuous-time stochastic semigroups. Our results apply both to cases…
I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie…
We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…
We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated…
A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…