Convergence rates for loop-erased random walk and other Loewner curves

We estimate convergence rates for curves generated by Loewner's differential equation under the basic assumption that a convergence rate for the driving terms is known. An important tool is what we call the tip structure modulus, a geometric measure of regularity for Loewner curves parameterized by capacity. It is analogous to Warschawski's boundary structure modulus and closely related to annuli crossings. The main application we have in mind is that of a random discrete-model curve approaching a Schramm-Loewner evolution (SLE) curve in the lattice size scaling limit. We carry out the approach in the case of loop-erased random walk (LERW) in a simply connected domain. Under mild assumptions of boundary regularity, we obtain an explicit power-law rate for the convergence of the LERW path toward the radial SLE$_2$ path in the supremum norm, the curves being parameterized by capacity. On the deterministic side, we show that the tip structure modulus gives a sufficient geometric condition for a Loewner curve to be H\"{o}lder continuous in the capacity parameterization, assuming its driving term is H\"{o}lder continuous. We also briefly discuss the case when the curves are a priori known to be H\"{o}lder continuous in the capacity parameterization and we obtain a power-law convergence rate depending only on the regularity of the curves.Comment: Published in at http://dx.doi.org/10.1214/13-AOP872 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Expectancy-Value Approach to Determinants of Trust

An Expectancy-Value model was used to test various attributes of trustworthiness, as determinants of people’s trust in 5 Swedish organizations (public and commercial). Trust was conceptualized as an attitude, dependent on respondents’ beliefs about and evaluations of the organization with respect to these attributes. A survey was sent out to a sample representative of the Swedish population (response rate: 55.5%; N = 347). It was found that the Expectancy-Value Model was powerful in explaining trust in 3 organizations. However, it was also found that a model including only values as predictors of trust was more powerful in explaining trust in 2 organizations: the Swedish Government and advertising firms. The phenomenon of double denial (Sjöberg & Montgomery, 1999) was very strong, which could be an important explanation of these findings. It is discussed whether double denial could be caused by trust ratings based on ideologies (e.g., political or general anti-business) subscribed to and emotional reactions, rather than analytical evaluations of an organization.trust; attitude; organizations; expectancy-value

Energy Policy Options - from the Perspective of Public Attitudes and Risk Perceptions

In the present study a representative sample (N = 797) of the Swedish population was surveyed, with regard to attitudes related to energy policy issues (e.g., environmental attitudes, risk perceptions, and attitudes towards different energy production systems) and self-reported electricity saving behavior. These factors were considered relevant in a Swedish energy policy context, because of the planned phase-out of nuclear power. Citizens’ attitudes have traditionally been important factors in energy policy-making, especially nuclear policy, and one of the conditions for a successful phase-out is increased levels of electricity savings among households and in industry, in order to compensate for the loss in energy production. Respondents reported positive attitudes to the environment in general and to electricity saving, while the attitudes to nuclear power as an energy production system in Sweden were relatively negative. Perceived risk was an important predictor of these attitudes and it was concluded that it is important to investigate mechanisms behind this variable. The relationship between attitudes towards electricity saving and electricity saving behavior was weak. It is discussed whether the contribution of psychological knowledge in energy conservation campaigns could be to elaborate on people’s willingness to be moral and public-spirited citizens in combination with their pro-environmental attitudes. This work was supported by grants from NUTEK and FRN. Viklund (1999) presented more data from the survey referred to here.energy policy; electricity saving; risk perception; attitudes; behavior

Interplay between Loewner and Dirichlet energies via conformal welding and flow-lines

The Loewner energy of a Jordan curve is the Dirichlet energy of its Loewner driving term. It is finite if and only if the curve is a Weil-Petersson quasicircle. In this paper, we describe cutting and welding operations on finite Dirichlet energy functions defined in the plane, allowing expression of the Loewner energy in terms of Dirichlet energy dissipation. We show that the Loewner energy of a unit vector field flow-line is equal to the Dirichlet energy of the harmonically extended winding. We also give an identity involving a complex-valued function of finite Dirichlet energy that expresses the welding and flow-line identities simultaneously. As applications, we prove that arclength isometric welding of two domains is sub-additive in the energy, and that the energy of equipotentials in a simply connected domain is monotone. Our main identities can be viewed as action functional analogs of both the welding and flow-line couplings of Schramm-Loewner evolution curves with the Gaussian free field.Comment: 28 pages, 3 figures. Minor revision according to referees' repor

Almost sure multifractal spectrum for the tip of an SLE curve

The tip multifractal spectrum of a two-dimensional curve is one way to describe the behavior of the uniformizing conformal map of the complement near the tip. We give the tip multifractal spectrum for a Schramm-Loewner evolution (SLE) curve, we prove that the spectrum is valid with probability one, and we give applications to the scaling of harmonic measure at the tip.Comment: 43 pages, 2 figure