1,720,964 research outputs found
On the Mixing Time of the 2D Stochastic Ising Model with "Plus" Boundary Conditions at Low Temperature
No full textWe consider the Glauber dynamics for the 2D Ising model in a box of side
L, at inverse temperature β and random boundary conditions τ whose distribution P
either stochastically dominates the extremal plus phase (hence the quotation marks in
the title) or is stochastically dominated by the extremal minus phase. A particular case is
when P is concentrated on the homogeneous configuration identically equal to + (equal
to −). For β large enough we show that for any ε > 0 there exists c = c(β, ε) such
that the corresponding mixing time Tmix satisfies limL→∞ P (Tmix ≥ exp(cLε)) = 0. In
the non-random case τ ≡ + (or τ ≡ −), this implies that Tmix ≤ exp(cLε). The same
bound holds when the boundary conditions are all + on three sides and all − on the
remaining one. The result, although still very far from the expected Lifshitz behavior
Tmix = O(L2), considerably improves upon the previous known estimates of the form
Tmix ≤ exp(cL
12
+ε). The techniques are based on induction over length scales, combined
with a judicious use of the so-called “censoring inequality” of Y. Peres and P. Winkler,
which in a sense allows us to guide the dynamics to its equilibrium measure
Dynamics of 2+1 dimensional SOS surfaces above a wall: slow mixing induced by entropic repulsion
No full textWe study the Glauber dynamics for the (2+1)d Solid-On-Solid model above a hard wall and below a far away ceiling, on an L × L box of Z2 with zero boundary conditions, at large inverse-temperature β. It was shown by Bricmont, El-Mellouki and Fro ̈hlich [12] that the floor constraint induces an entropic repulsion effect which lifts the surface to an average height H ≍ (1/β) log L. As an essential step in understanding the effect of entropic repulsion on the Glauber dynamics we determine the equilibrium height H to within an additive constant: H = (1/4β) log L+O(1). We then show that starting from zero initial conditions the surface rises to its final height H through a sequence of metastable transitions between consecutive levels. The time for a transition from height h = aH , a ∈ (0, 1), to height h + 1 is roughly exp(cLa ) for some constant c > 0. In particular, the mixing time of the dynamics is exponentially large in L, i.e. Tmix ecL. We also provide the matching upper bound Tmix ec′L, requiring a challenging analysis of the statistics of height contours at low temperature and new coupling ideas and techniques. Finally, to emphasize the role of entropic repulsion we show that without a floor constraint at height zero the mixing time is no longer exponentially large in L
"Zero" Temperature Stochastic 3D Ising Model and Dimer Covering Fluctuations: A First Step Towards Interface Mean Curvature Motion
No full text"We consider the Glauber dynamics for the Ising model with "+" boundary conditions, at zero temperature or at a temperature that goes to zero with the system size (hence the quotation marks in the title). In dimension d = 3 we prove that an initial domain of linear size L of "-" spins disappears within a time tau(+), which is at most L(2)(log L)(c) and at least L(2)\/(c log L) for some c > 0. The proof of the upper bound proceeds via comparison with an auxiliary dynamics which mimics the motion by mean curvature that is expected to describe, on large time scales, the evolution of the interface between "+" and "-" domains. The analysis of the auxiliary dynamics requires recent results on the fluctuations of the height function associated to dimer coverings of the infinite honeycomb lattice. Our result, apart from the spurious logarithmic factors, is the first rigorous confirmation of the Lifshitz law tau(+) similar or equal to const x L(2), conjectured on heuristic grounds [8, 13]. In dimension d = 2, tau(+) can be shown to be of order L(2) without logarithmic corrections: the upper bound was proven in [6], and here we provide the lower bound. For d = 2, we also prove that the spectral gap of the generator behaves like c\/L for L large, as conjectured in [2]. (C) 2010 Wiley Periodicals, Inc.
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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