Is breaking of ensemble equivalence monotone in the number of constraints?

Breaking of ensemble equivalence between the microcanonical ensemble and the canonical ensemble may occur for random graphs whose size tends to infinity, and is signaled by a non-zero specific relative entropy between the two ensembles. In Garlaschelli et al. (2017) and Garlaschelli et al. (0000) it was shown that breaking occurs when the constraint is put on the degree sequence (configuration model). It is not known what is the effect on the relative entropy when the number of constraints is reduced, i.e., when only part of the nodes are constrained in their degree (and the remaining nodes are left unconstrained). Intuitively, the relative entropy is expected to decrease. However, this is not a trivial issue because when constraints are removed both the microcanonical ensemble and the canonical ensemble change. In this paper a formula for the relative entropy valid for generic discrete random structures, recently formulated by Squartini and Garlaschelli, is used to prove that the relative entropy is monotone in the number of constraints when the constraint is on the degrees of the nodes. It is further shown that the expression for the relative entropy corresponds, in the dense regime, to the degrees in the microcanonical ensemble being asymptotically multivariate Dirac and in the canonical ensemble being asymptotically Gaussian.     

Random locations of periodic stationary processes

We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that the set of all possible distributions of intrinsic location functionals for periodic stationary processes is the convex hull generated by a specific group of distributions. We then focus on two special subclasses of these random locations. For the first subclass, the density has a uniform lower bound; for the second subclass, the possible distributions are closely related to the concept of joint mixability.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

一类随机环境中的随机游动

研究了在环境平稳遍历时,右半直线上可逗留的随机环境中的随机游动的常返性和非常返性,给出非常返、正常返、零常返的充要条件,并讨论了极限性质.作为推论,给出P独立同分布时的相应结论.     

Set-valued dynamic systems and random iterations of set-valued weaker contractions in uniform spaces

Set-valued weaker contractions in uniform, locally convex and metric spaces are defined and dynamic systems of such weaker contractions are studied. Conditions guaranteeing the convergence of generalized sequences of random iterations and iterations and the existence and uniqueness of endpoints of set-valued weaker contractions are established. Our definitions and results are new for set-valued maps in uniform, locally convex and metric spaces and even for single-valued maps.     

BMO from dyadic BMO via expectations on product spaces of homogeneous type

Using the random dyadic lattices developed by Hytönen and Kairema, we build up a bridge between BMO and dyadic BMO, and hence one between VMO and dyadic VMO, via expectations over dyadic lattices on spaces of homogeneous type, including both the one-parameter and product cases. We also obtain a similar relationship between _Ap$A_p$ and dyadic _Ap$A_p$, as well as one between the reverse Hölder class _RHp${\mathit{RH}}_p$ and dyadic _RHp${\mathit{RH}}_p$, via geometric–arithmetic expectations. These results extend the earlier theory along this line, developed by Garnett, Jones, Pipher, Ward, Xiao and Treil, to the more general setting of spaces of homogeneous type in the sense of Coifman and Weiss.     

Post buckling response of functionally graded materials plate subjected to mechanical and thermal loadings with random material properties

In this paper, the second order statistics of post buckling response of functionally graded materials plate (FGM) subjected to mechanical and thermal loading with nonuniform temperature changes subjected to temperature independent (TID) and dependent (TD) material properties is examined. Material properties such as material properties of each constituent’s materials, volume fraction index are taken as independent random input variables. The basic formulation is based on higher order shear deformation theory (HSDT) with von-Karman nonlinear kinematic using modified C⁰ continuity. A direct iterative based C⁰ nonlinear finite element method (FEM) combined with mean centered first order perturbation technique (FOPT) proposed by last two authors for the composite plate is extended for Functionally Graded Materials (FGMs) plate with reasonable accuracy to compute the second order statistics (mean and coefficient of variation) of the post buckling load response of the FGM plates. The effect of random material properties with amplitude ratios, volume fraction index, plate thickness ratios, aspect ratios, boundary conditions and types of loadings subjected to TID and TD material properties are presented through numerical examples. The performance of outlined present approach is validated with the results available in literatures and independent Monte Carlo simulation (MCS).     

On a New Class of Systems of Generalized Quasi-Variational Inequalities

We introduce new types of systems of generalized quasi-variational inequalities and we prove the existence of the solutions by using results of pair equilibrium existence for free abstract economies. We consider the fuzzy models and we also introduce the random free abstract economy and the random equilibrium pair. The existence of the solutions for the systems of quasi-variational inequalities comes as consequences of the existence of equilibrium pairs for the considered free abstract economies.     

Random Variable Generation Using Concavity Properties of Transformed Densities

Abstract

Algorithms are developed for constructing random variable generators for families of densities. The generators depend on the concavity structure of a transformation of the density. The resulting algorithms are rejection algorithms and the methods of this article are concerned with constructing good rejection algorithms for general densities.