Multicritical continuous random trees

We introduce generalizations of Aldous' Brownian Continuous Random Tree as scaling limits for multicritical models of discrete trees. These discrete models involve trees with fine-tuned vertex-dependent weights ensuring a k-th root singularity in their generating function. The scaling limit involves continuous trees with branching points of order up to k+1. We derive explicit integral representations for the average profile of this k-th order multicritical continuous random tree, as well as for its history distributions measuring multi-point correlations. The latter distributions involve non-positive universal weights at the branching points together with fractional derivative couplings. We prove universality by rederiving the same results within a purely continuous axiomatic approach based on the resolution of a set of consistency relations for the multi-point correlations. The average profile is shown to obey a fractional differential equation whose solution involves hypergeometric functions and matches the integral formula of the discrete approach.Comment: 34 pages, 12 figures, uses lanlmac, hyperbasics, eps

Cutoff for the East process

The East process is a 1D kinetically constrained interacting particle system, introduced in the physics literature in the early 90's to model liquid-glass transitions. Spectral gap estimates of Aldous and Diaconis in 2002 imply that its mixing time on $L$ sites has order $L$. We complement that result and show cutoff with an $O(\sqrt{L})$-window. The main ingredient is an analysis of the front of the process (its rightmost zero in the setup where zeros facilitate updates to their right). One expects the front to advance as a biased random walk, whose normal fluctuations would imply cutoff with an $O(\sqrt{L})$-window. The law of the process behind the front plays a crucial role: Blondel showed that it converges to an invariant measure $\nu$, on which very little is known. Here we obtain quantitative bounds on the speed of convergence to $\nu$, finding that it is exponentially fast. We then derive that the increments of the front behave as a stationary mixing sequence of random variables, and a Stein-method based argument of Bolthausen ('82) implies a CLT for the location of the front, yielding the cutoff result. Finally, we supplement these results by a study of analogous kinetically constrained models on trees, again establishing cutoff, yet this time with an $O(1)$-window.Comment: 33 pages, 2 figure

A max-type recursive model: some properties and open questions

We consider a simple max-type recursive model which was introduced in the study of depinning transition in presence of strong disorder, by Derrida and Retaux. Our interest is focused on the critical regime, for which we study the extinction probability, the first moment and the moment generating function. Several stronger assertions are stated as conjectures.Comment: A version accepted to Charles Newman Festschrift (to appear by Springer

THE INFLUENCE OF STUDENT BACKGROUND CHARACTERISTICS ON PROFICIENCY IN ENGLISH AS A FOREIGN LANGUAGE: INDONESIAN CONTEXT

In order to explain differences in English proficiency level, one needs to consider a number of factors frequently considered important at a variety of level of education systems. Among the factors that operate to influence English Foreign Language Proficiency are those associated with the student background variables. This study identifies the student level factors that influence English Foreign Language Proficiency. It is expected that this study can contribute to the development of a theory of foreign language learning that applies to students studying the English language at other universities in Indonesia and South-East Asia. This study involves the employment of an exploratory approach for the examination of the relationships between variables operating at the student level. Data are analyzed using Partial Least Squares Path Analysis (PLSPATH) to identify in an exploratory way the variables that have significant direct and indirect effects on English Foreign Language Proficiency. The study shows that a number of student background characteristics such as sex of student (GENDER), socio-economic of student (SES), Faculty of Instruction (FACULTY), score of English 1 (ENGLISH_1) and semester in which students enrol in English 2 (SEMESTER) have only direct effects on English Language Proficiency, while student prior achievement (PRIOR) has both direct and indirect effects on English Foreign Language Proficienc

THE INFLUENCE OF STUDENT BACKGROUND CHARACTERISTICS ON PROFICIENCY IN ENGLISH AS A FOREIGN LANGUAGE: INDONESIAN CONTEXT

In order to explain differences in English proficiency level, one needs to consider a number of factors frequently considered important at a variety of level of education systems. Among the factors that operate to influence English Foreign Language Proficiency are those associated with the student background variables. This study identifies the student level factors that influence English Foreign Language Proficiency. It is expected that this study can contribute to the development of a theory of foreign language learning that applies to students studying the English language at other universities in Indonesia and South-East Asia. This study involves the employment of an exploratory approach for the examination of the relationships between variables operating at the student level. Data are analyzed using Partial Least Squares Path Analysis (PLSPATH) to identify in an exploratory way the variables that have significant direct and indirect effects on English Foreign Language Proficiency. The study shows that a number of student background characteristics such as sex of student (GENDER), socio-economic of student (SES), Faculty of Instruction (FACULTY), score of English 1 (ENGLISH_1) and semester in which students enrol in English 2 (SEMESTER) have only direct effects on English Language Proficiency, while student prior achievement (PRIOR) has both direct and indirect effects on English Foreign Language Proficienc

Dynamic critical exponents of Swendsen-Wang and Wolff algorithms by nonequilibrium relaxation

With a nonequilibrium relaxation method, we calculate the dynamic critical exponent z of the two-dimensional Ising model for the Swendsen-Wang and Wolff algorithms. We examine dynamic relaxation processes following a quench from a disordered or an ordered initial state to the critical temperature T_c, and measure the exponential relaxation time of the system energy. For the Swendsen-Wang algorithm with an ordered or a disordered initial state, and for the Wolff algorithm with an ordered initial state, the exponential relaxation time fits well to a logarithmic size dependence up to a lattice size L=8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponent z_exp=1.19(2) up to L=2048. For comparison, we also compute the effective dynamic exponents through the integrated correlation times. In addition, an exact result of the Swendsen-Wang dynamic spectrum of a one-dimension Ising chain is derived.Comment: 13 pages, 6 figure

Particle Systems with Stochastic Passing

We study a system of particles moving on a line in the same direction. Passing is allowed and when a fast particle overtakes a slow particle, it acquires a new velocity drawn from a distribution P_0(v), while the slow particle remains unaffected. We show that the system reaches a steady state if P_0(v) vanishes at its lower cutoff; otherwise, the system evolves indefinitely.Comment: 5 pages, 5 figure