Random walks reaching against all odds the other side of the quarter plane

For a homogeneous random walk in the quarter plane with nearest-neighbor transitions, starting from some state $(i_0,j_0)$, we study the event that the walk reaches the vertical axis, before reaching the horizontal axis. We derive an exact expression for the probability of this event, and derive an asymptotic expression for the case when $i_0$ becomes large, a situation in which the event becomes highly unlikely. The exact expression follows from the solution of a boundary value problem and is in terms of an integral that involves a conformal gluing function. The asymptotic expression follows from the asymptotic evaluation of this integral. Our results find applications in a model for nucleosome shifting, the voter model and the asymmetric exclusion process.Comment: 18 pages, 2 figures, to appear in Journal of Applied Probabilit

Phase diagram of a generalized ABC model on the interval

We study the equilibrium phase diagram of a generalized ABC model on an interval of the one-dimensional lattice: each site $i=1,...,N$ is occupied by a particle of type \a=A,B,C, with the average density of each particle species N_\a/N=r_\a fixed. These particles interact via a mean field non-reflection-symmetric pair interaction. The interaction need not be invariant under cyclic permutation of the particle species as in the standard ABC model studied earlier. We prove in some cases and conjecture in others that the scaled infinite system N\rw\infty, i/N\rw x\in[0,1] has a unique density profile \p_\a(x) except for some special values of the r_\a for which the system undergoes a second order phase transition from a uniform to a nonuniform periodic profile at a critical temperature $T_c=3\sqrt{r_A r_B r_C}/2\pi$.Comment: 25 pages, 6 figure

Phase fluctuations in the ABC model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations

On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature

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

Entrepreneurial intention studies: A hybrid bibliometric method to identify new directions for theory and research

Fragmentation is the main obstacle to scientific progress on entrepreneurial intention. To address this issue, we systematise the current literature with a hybrid bibliometric method that combines co-citation and bibliographic coupling analysis for the first time in entrepreneurial intention studies to show the field's knowledge base and research fronts and to examine how divergent perspectives have challenged the core knowledge of the field. We highlight three recurring dimensions of entrepreneurial intention studies: (1) personal factors, (2) social factors and (3) investigational settings. In addition to introducing new constructs, divergent perspectives have emphasised the interplay between these components and challenged the mechanisms connecting them. Based on these findings, we extend previous classifications in the literature by providing a framework that integrates divergent perspectives with the field's knowledge base, helping establish future research avenues and improving the theorising process of entrepreneurial intention

Spacecraft VLBI tracking to enhance stellar occultations astrometry of planetary satellites

Stellar occultations currently provide the most accurate ground-based measurements of the positions of natural satellites (down to a few kilometres for the Galilean moons). However, when using these observations in the calculation of satellite ephemerides, the uncertainty in the planetary ephemerides dominates the error budget of the occultation. We quantify the local refinement in the central planet's position achievable by performing Very Long Baseline Interferometry (VLBI) tracking of an in-system spacecraft temporally close to an occultation. We demonstrate the potential of using VLBI to enhance the science return of stellar occultations for satellite ephemerides. We identified the most promising observation and tracking opportunities offered by the Juno spacecraft around Jupiter as perfect test cases, for which we ran simulations of our VLBI experiment. VLBI tracking at Juno's perijove close to a stellar occultation locally (in time) reduces the uncertainty in Jupiter's angular position in the sky to 250-400 m. This represents up to an order of magnitude improvement with respect to current solutions and is lower than the stellar occultation error, thus allowing the moon ephemeris solution to fully benefit from the observation. Our simulations showed that the proposed tracking and observation experiment can efficiently use synergies between ground- and space-based observations to enhance the science return on both ends. The reduced error budget for stellar occultations indeed helps to improve the moons' ephemerides, which in turn benefit planetary missions and their science products, such as the recently launched JUICE and upcoming Europa Clipper missions