The q-PushASEP: A New Integrable Model for Traffic in 1+1 Dimension

We introduce a new interacting (stochastic) particle system q-PushASEP which interpolates between the q-TASEP introduced by Borodin and Corwin (see arXiv:1111.4408, and also arXiv:1207.5035; arXiv:1305.2972; arXiv:1212.6716) and the q-PushTASEP introduced recently by Borodin and Petrov (arXiv:1305.5501). In the q-PushASEP, particles can jump to the left or to the right, and there is a certain partially asymmetric pushing mechanism present. This particle system has a nice interpretation as a model of traffic on a one-lane highway in which cars are able to accelerate or slow down. Using the quantum many body system approach, we explicitly compute the expectations of a large family of observables for this system in terms of nested contour integrals. We also discuss relevant Fredholm determinantal formulas for the distribution of the location of each particle, and connections of the model with a certain two-sided version of Macdonald processes and with the semi-discrete stochastic heat equation.Comment: 22 pages; 4 figures. v2: minor improvements of presentation and discussions. To appear in Journal of Statistical Physic

Statistical profile of the self-employed in Bulgaria

This report presents the statistical self-employed profile in Bulgaria. It is based on Eurostat data on the labour force in 2017 and a study on self-employment in Bulgaria by the Bulgarian National Statistical Institute. A comparative study analyses self-employment criteria across Bulgaria, countries within and outside of the EU, as well as the profile of the self-employed: across industries, gender, customer base, reasons to start a business, main challenges, intentions to retain or change status, generation of employment, organizational dependence

Spectral theory for the q-Boson particle system

We develop spectral theory for the generator of the q-Boson (stochastic) particle system. Our central result is a Plancherel type isomorphism theorem for this system. This theorem has various implications. It proves the completeness of the Bethe ansatz for the q-Boson generator and consequently enables us to solve the Kolmogorov forward and backward equations for general initial data. Owing to a Markov duality with q-TASEP, this leads to moment formulas which characterize the fixed time distribution of q-TASEP started from general initial conditions. The theorem also implies the biorthogonality of the left and right eigenfunctions. We consider limits of our q-Boson results to a discrete delta Bose gas considered previously by van Diejen, as well as to another discrete delta Bose gas that describes the evolution of moments of the semi-discrete stochastic heat equation (or equivalently, the O'Connell-Yor semi-discrete directed polymer partition function). A further limit takes us to the delta Bose gas which arises in studying moments of the stochastic heat equation / Kardar-Parisi-Zhang equation.Comment: 63 pages, 5 figure

Contribution to the myrmecofauna (Formicidae, Hymenoptera) of Mt. Kopaonik (Serbia)

The myrmecofauna of Serbia is still insufficiently investigated. In the past ants were not a challenge for the entomologists of Serbia, only a few of which paid attention to ants and registered some ant species among other insect species. Živojinović (1950) registered 18 species of ants in the forest region of Majdanpek (Serbia), although he considered some valid species (Lasius alienus, L. brunneus, Camponotus herculeanus, and Formica pratensis) as subspecies. Vogrin (1955) elaborated Hymenoptera Aculeata of Yugoslavia, and registered 16 species of ants in Serbia (Srem). Gradojević (1963) listed 11 species of ants of Deliblatska Peščara (Deliblato Sands) (Vojvodina, Serbia)