相关论文: Moderate deviations for random fields and random c…
We study deformations of complex projective varieties that are homotopically or homologically trivial. We formulate several conjectures and give some examples and partial answers.
We show the existence of prime divisors computing minimal log discrepancies in positive characteristic except for a special case. Moreover we prove the lower semicontinuity of minimal log discrepancies for smooth varieties in positive…
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie Weiss model (i.e., standard Curie-Weiss model embedded in a site dependent, i.i.d. random environment). We obtain path space large…
We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes.…
The paper contains an exposition of recent as well as old enough results on determinantal random point fields. We start with some general theorems including the proofs of the necessary and sufficient condition for the existence of the…
We derive the necessary and sufficient condition for almost sure convergence of the sequence of measurable functions, and consider some applications in the theory of Fourier series and in the theory of random fields.
New sum and product uncertainty relations, containing variances of three or four observables, but not containing explicitly their covariances, are derived. One of consequences is the new inequality, giving a nonzero lower bound for the…
Differentiations of operator algebras over non-archimedean spherically complete fields are investigated. Theorems about a differentiation being internal are demonstrated.
We give a general setting for Cram\'er's large deviations theorem for the empirical means of a field of random vectors, which contains Cram\'er's theorem for i.i.d. random vectors and Sanov's theorem for asymptotically decoupled measures.…
We investigate systems of interacting stochastic differential equations with two kinds of heterogeneity: one originating from different weights of the linkages, and one concerning their asymptotic relevance when the system becomes large. To…
We define generalized vector fields, and contraction and Lie derivatives with respect to them. Generalized commutators are also defined.
Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…
In this paper we present some extensions of recent noncentral moderate deviation results in the literature. In the first part we generalize the results in \cite{BeghinMacciSPL2022} by considering a general L\'evy process $\{S(t):t\geq 0\}$…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…
We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.
We study the equilibrium fluctuations for a gradient exclusion process with conductances in random environments, which can be viewed as a central limit theorem for the empirical distribution of particles when the system starts from an…
A simple implementation of Noether's theorem for discrete symmetries in relativistic continuum field theories is presented. The associated conserved current is exemplified by charge conjugation and a cyclic symmetry. In addition, the…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
We provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is…
We introduce a version of discrete Morse theory for posets. This theory studies the topology of the order complexes K(X) of h-regular posets X from the critical points of admissible matchings on X. Our approach is related to R. Forman's…