Equilibrium fluctuations of additive functionals of zero-range models

For mean-zero and asymmetric zero-range processes on $\Z^d$, the fluctuations of additive functionals starting from an invariant measure are considered. Under certain assumptions, we establish when the fluctuations are diffusive and satisfy functional central limit theorems. These results complement those for symmetric zero-range systems and also those for simple exclusion models already in the literature.FC

Special Session: Gazing into the shadows: Contemplating the research agenda for the dark side of brands and branding

Branding is one of the essential pillars of marketing, but not everything that brands represent is positive. Indeed, a considerable amount of brand-related activities takes place in the shadowy periphery of society. The purpose of this special session is to explore these darker sides of brands and branding and to spotlight a future research agenda related to two distinct yet interrelated trends—brands embracing the shadows and the shadows embracing branding. Brand researchers and managers recognize brands as complex, multifaceted entities that possess “good” and “ugly” qualities (Fitzsimons 2015). Some of the recently explored darker sides of brands and branding include links between brand attachment and community conflict manifested in oppositional “trash-talking” and “schadenfreude” feelings of pleasure for the opposition’s misfortune (e.g., Ewing et al. 2013; Hickman and Ward 2007; Japutra et al. 2014) and brands’ ability as cultural artifacts to invoke or exacerbate the vulnerability of individuals and communities who may feel ignored or misrepresented in brand communications (Kipnis et al. 2013; Schroeder and Borgerson 2005; Yang 2011). At the same time, revealing the darker side of a brand’s identity and then utilizing that revelation strategically to enhance perceptions of brand sincerity and authenticity is a growing trend in practitioner discourse (Silk 2015; Yakob 2015). Hence, there is a need for more research and critical reflection on brands in legitimate market contexts embracing their shadowy dimensions. On a related note, considerably less attention has been paid to the effects of legitimate branding techniques when utilized by “the darker side” of business, i.e., illegitimate market actors. However, a handful of pioneering studies demonstrate that branding strategies are being exploited by terrorist and drug trade groups (Breazeale et al. 2015; Kipnis et al. 2015; O’Sullivan 2014). Recently emerged findings explore the negative societal outcomes that result when branding strategies are applied in these contexts by organizations and individuals with more nefarious goals. The effects range from extremely harmful to the broader society (e.g., building awareness, reputation, and notoriety through brand identities that project power and strength—Breazeale et al. 2015; Kipnis et al. 2015) to mitigating potential risks to individual consumers (i.e., serving as means of differentiation, enabling consumers to generate and exchange information on degrees of risk associated with the consumption of particular brands—O’Sullivan 2014). In addition, practitioner research and media reports point to indirect risks that illegitimate actors embracing the power of branding pose to legitimate brands. Such risks encompass the ambush of established brand names for the marketing of illegitimate products. One such example received prominent media coverage when LeBron James heroin was introduced to the market in a twisted take on the power of celebrity brands (Palmer 2012). The session brings together branding, marketing strategy, and transformative consumer research scholars, to reflect upon recent theoretical and empirical advances and debate the future research agenda for the following two research streams: (1) the darker side of legitimate brands and (2) the darker side of branding as enacted by illegitimate market actors. The session is structured to present two studies contributing to each stream. Specifically, Japutra and Ekinci identify coping strategies deployed by consumers to deal with such negative consequences of legitimate branding as a perceived failure in self-brand relationship. Canhoto, Dibb, Nguyen, and Simkin shed light on how such failure perceptions can be triggered by dishonest and exploitative actions of legitimate firms and propose a framework that captures how the dark intentions and behaviors exhibited by organizations provoke and exacerbate consumer anguish and retaliation. Kipnis, Pullig, and Bebek offer insights into how wholesale drug trade actors effectively utilize visual brand identity signaling practices to build distinctiveness and credibility within their supply chains, posing a framework for these brands’ devalue. Breazeale and colleagues identify that the factors contributing to notoriety of violent extremist organizations are comparable to factors contributing to brand reputation of legitimate business organizations. The session highlights that exploitation of the dark side of brands is a growing concerning trend that poses significant threats to well-being of societies and demonstrates the need and the value of greater marketing research input in addressing this evolving problem

A particle system with explosions: law of large numbers for the density of particles and the blow-up time

Consider a system of independent random walks in the discrete torus with creation-annihilation of particles and possible explosion of the total number of particles in finite time. Rescaling space and rates for diffusion/creation/annihilation of particles, we obtain a stong law of large numbers for the density of particles in the supremum norm. The limiting object is a classical solution to the semilinear heat equation u_t =u_{xx} + f(u). If f(u)=u^p, 1<p \le 3, we also obtain a law of large numbers for the explosion time

Invariant Measures and Convergence for Cellular Automaton 184 and Related Processes

For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of the hydrodynamic limit. The most widely known representatives of this class of automata are: Automaton 184 from the classification of S. Wolfram, an annihilating particle system and a surface growth model.Comment: 18 page

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics

We present a lattice gas model that without fine tuning of parameters is expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ) universality class. To this end, we review briefly how non-linear fluctuating hydrodynamics in one dimension predicts that all dynamical universality classes in its range of applicability belong to an infinite discrete family which we call Fibonacci family since their dynamical exponents are the Kepler ratios $z_i = F_{i+1}/F_{i}$ of neighbouring Fibonacci numbers $F_i$, including diffusion ($z_2=2$), KPZ ($z_3=3/2$), and the limiting ratio which is the golden mean $z_\infty=(1+\sqrt{5})/2$. Then we revisit the case of two conservation laws to which the modified KPZ model belongs. We also derive criteria on the macroscopic currents to lead to other non-KPZ universality classes.Comment: 17 page

Classical phase transitions in a one-dimensional short-range spin model

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.Comment: 29 pages, 11 figure

Phase diagram of the ABC model on an interval

The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a one-dimensional lattice of N sites with closed (zero flux) boundaries. In this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical Gibbs measure with long range asymmetric pair interactions. This generalizes results for the ring case, where detailed balance holds, and in fact the steady state measure is known only for the case of equal densities of the different species: in the latter case the stationary states of the system on a ring and on an interval are the same. We prove that in the N to infinity limit the scaled density profiles are given by (pieces of) the periodic trajectory of a particle moving in a quartic confining potential. We further prove uniqueness of the profiles, i.e., the existence of a single phase, in all regions of the parameter space (of average densities and temperature) except at low temperature with all densities equal; in this case a continuum of phases, differing by translation, coexist. The results for the equal density case apply also to the system on the ring, and there extend results of Clincy et al.Comment: 52 pages, AMS-LaTeX, 8 figures from 10 eps figure files. Revision: minor changes in response to referee reports; paper to appear in J. Stat. Phy

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density \rho_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters