Effects of the climate change on regional ozone dry deposition

This impact study investigates connections between the regional climate change and the tropospheric ozone deposition over different vegetations in Hungary due to the possible changes of atmospheric and environmental properties. The spatial and temporal variability of the dry deposition velocity of ozone was estimated for different time periods (1961–1990 for reference period and two future scenarios: 2021–2050 and 2071–2100). Simulations were performed with a sophisticated deposition model using the RegCM regional climate model results as an input. We found a significant reduction of the ozone deposition velocities during summer months, which predicts less ozone damage to the vegetation in the future. However elevated ozone concentration and changed plant physiology can compensate the effect of this reduction

Spatial and temporal variability of ozone deposition

Soil moisture and ozone deposition velocity under continental climate conditions were estimated using a newly developed algorithm. The relationship between soil moisture and deposition velocity was investigated and analysed. These results emphasize the importance of a sophisticated parameterization of soil moisture in surface-atmosphere interaction processes

A pedestrian's view on interacting particle systems, KPZ universality, and random matrices

These notes are based on lectures delivered by the authors at a Langeoog seminar of SFB/TR12 "Symmetries and universality in mesoscopic systems" to a mixed audience of mathematicians and theoretical physicists. After a brief outline of the basic physical concepts of equilibrium and nonequilibrium states, the one-dimensional simple exclusion process is introduced as a paradigmatic nonequilibrium interacting particle system. The stationary measure on the ring is derived and the idea of the hydrodynamic limit is sketched. We then introduce the phenomenological Kardar-Parisi-Zhang (KPZ) equation and explain the associated universality conjecture for surface fluctuations in growth models. This is followed by a detailed exposition of a seminal paper of Johansson that relates the current fluctuations of the totally asymmetric simple exclusion process (TASEP) to the Tracy-Widom distribution of random matrix theory. The implications of this result are discussed within the framework of the KPZ conjecture.Comment: 52 pages, 4 figures; to appear in J. Phys. A: Math. Theo

First passage percolation on random graphs with infinite variance degrees

We prove non-universality results for first-passage percolation on the configuration model with i.i.d. degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of the weight distribution, we use an example-based approach and show that rather different behaviors are possible. When the weights are a.s. larger than a constant, the weight and number of edges in the graph grow proportionally to loglog(n), as for the graph distances. On the other hand, when the continuous-time branching process describing the first passage percolation exploration through the graph reaches infinitely many vertices in finite time, the weight converges to the sum of two i.i.d. random variables representing the explosion times of the processes started from the two sources. This non-universality is in sharp contrast to the setting where the degree sequence has a finite variance (see Bhamidi, Hofstad and Hooghiemstra arXiv: 1210.6839)

Fixed speed competition on the configuration model with infinite variance degrees: unequal speeds

\u3cp\u3eWe study competition of two spreading colors starting from single sources on the configuration model with i.i.d. degrees following a power-law distribution with exponent τ ∈ (2, 3). In this model two colors spread with a fixed but not necessarily equal speed on the unweighted random graph. We show that if the speeds are not equal, then the faster color paints almost all vertices, while the slower color can paint only a random subpolynomial fraction of the vertices. We investigate the case when the speeds are equal and typical distances in a follow-up paper.\u3c/p\u3

Nonuniversality of weighted random graphs with infinite variance degree

\u3cp\u3eWe prove nonuniversality results for first-passage percolation on the configuration model with independent and identically distributed (i.i.d.) degrees having infinite variance. We focus on the weight of the optimal path between two uniform vertices. Depending on the properties of the weight distribution, we use an example-based approach and show that rather different behaviours are possible. When the weights are almost surely larger than a constant, the weight and number of edges in the graph grow proportionally to log log n, as for the graph distances. On the other hand, when the continuous-time branching process describing the first-passage percolation exploration through the graph reaches infinitely many vertices in finite time, the weight converges to the sum of two i.i.d. random variables representing the explosion times of the continuous-time processes started from the two sources. This nonuniversality is in sharp contrast to the setting where the degree sequence has a finite variance, Bhamidi et al. (2012).\u3c/p\u3

Tight fluctuations of weight-distances in random graphs with infinite-variance degrees

\u3cp\u3eWe prove results for first-passage percolation on the configuration model with degrees having asymptotic finite mean, infinite variance and i.i.d. edge-weights with strictly positive support of the form Y= a+ X, where a is a positive constant and the excess edge-weight X is a non-negative random variable with zero as the infimum of its support. We prove that the weight of the optimal path between two uniformly chosen vertices has tight fluctuations around the asymptotic mean of the graph-distance if and only if the following condition holds: the random variable X is such that the age-dependent branching process describing first-passage percolation exploration in the same graph with edge-weights from distribution X has a positive probability to reach infinitely many individuals in a finite time. This shows that almost-shortest paths in the graph-distance proliferate, in the sense that there even exist paths having tight total excess edge-weight for appropriate edge-weight distributions. Our proof makes use of a degree-dependent percolation model that we believe is interesting in its own right, as well as tightness results for distances in scale-free configuration models that we prove to hold under rather weak conditions on the degrees.\u3c/p\u3

When is a Scale-Free Graph Ultra-Small?

In this paper we study typical distances in the configuration model, when the degrees have asymptotically infinite variance. We assume that the empirical degree distribution follows a power law with exponent $\tau\in (2,3)$, up to value $n^{\beta_n}$ for some $\beta_n\gg (\log n)^{-\gamma}$ and $\gamma\in(0,1)$. This assumption is satisfied for power law i.i.d. degrees, and also includes truncated power-law distributions where the (possibly exponential) truncation happens at $n^{\beta_n}$. We show that the graph distance between two uniformly chosen vertices centers around $2 \log \log (n^{\beta_n}) / |\log (\tau-2)| + 1/(\beta_n(3-\tau))$, with tight fluctuations. Thus, the graph is an \emph{ultrasmall world} whenever $1/\beta_n=o(\log\log n)$. We determine the distribution of the fluctuations around this value, in particular we prove that these are non-converging tight random variables that show $\log \log$-periodicity. We describe the topology and number of shortest paths: We show that the number of shortest paths is of order $n^{f_n\beta_n}$, where $f_n \in (0,1)$ is a random variable that oscillates with $n$. The two end-segments of any shortest path have length $\log \log (n^{\beta_n}) / |\log (\tau-2)|$+tight, and the total degree is increasing towards the middle of the path on these segments. The connecting middle segment has length $1/(\beta_n(3-\tau))$+tight, and it contains only vertices with degree at least of order $n^{(1-f_n)\beta_n}$, thus all the degrees on this segment are comparable to the maximal degree. Our theorems also apply when instead of truncating the degrees, we start with a configuration model and we remove every vertex with degree at least $n^{\beta_n}$, and the edges attached to these vertices. This sheds light on the attack vulnerability of the configuration model with infinite variance degrees.Comment: 36 pages, 1 figur