11 results
Search Results
Now showing 1 - 10 of 11
- ItemLocalization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model([Madralin] : EMIS ELibEMS, 2018) Flegel, FranziskaWe study the asymptotic behavior of the principal eigenvector and eigenvalue of the random conductance Laplacian in a large domain of Zd (d≥2) with zero Dirichlet condition. We assume that the conductances w are positive i.i.d. random variables, which fulfill certain regularity assumptions near zero. If γ=sup{q≥0:E[w−q]<∞}<1/4, then we show that for almost every environment the principal Dirichlet eigenvector asymptotically concentrates in a single site and the corresponding eigenvalue scales subdiffusively. The threshold γc=1/4 is sharp. Indeed, other recent results imply that for γ>1/4 the top of the Dirichlet spectrum homogenizes. Our proofs are based on a spatial extreme value analysis of the local speed measure, Borel-Cantelli arguments, the Rayleigh-Ritz formula, results from percolation theory, and path arguments.
- ItemBilateral Trade Agreements and the Interconnectedness of Global Trade(Lausanne : Frontiers Media, 2018) Maluck, Julian; Glanemann, Nicole; Donner, Reik V.Over the last decades, bilateral trade agreements (BTAs) have increased considerably in number and economic relevance. Notably, such agreements substantially affect global trade, since the reorganization of flows of goods and services has prominent impacts on the contracting countries' economies, but also on other parties that are (directly or indirectly) engaged in trade with these countries. Here, we empirically study the effect of BTAs on the input-output linkages between the contractual parties' national economic sectors by defining a new measure of Trade Interconnectedness (TI), which describes the relative importance of direct and indirect production linkages between the two countries in the international trade network. By analyzing its time evolution for each pair of trade agreement partners, we demonstrate that while most BTAs are succeeded by an increase in TI between the contractors, there are some notable exceptions. In particular, comparing the trade profiles of China and the United States (US), we find indications that both countries have been pursuing fundamentally different objectives and strategies related to the negotiation of BTAs.
- ItemTracking online topics over time: understanding dynamic hashtag communities(New York, NY [u.a.] : Springer international, 2018) Lorenz-Spreen, Philipp; Wolf, Frederik; Braun, Jonas; Ghoshal, Gourab; Djurdjevac Conrad, Nataša; Hövel, PhilippBackground: Hashtags are widely used for communication in online media. As a condensed version of information, they characterize topics and discussions. For their analysis, we apply methods from network science and propose novel tools for tracing their dynamics in time-dependent data. The observations are characterized by bursty behaviors in the increases and decreases of hashtag usage. These features can be reproduced with a novel model of dynamic rankings. Hashtag communities in time: We build temporal and weighted co-occurrence networks from hashtags. On static snapshots, we infer the community structure using customized methods. On temporal networks, we solve the bipartite matching problem of detected communities at subsequent timesteps by taking into account higher-order memory. This results in a matching protocol that is robust toward temporal fluctuations and instabilities of the static community detection. The proposed methodology is broadly applicable and its outcomes reveal the temporal behavior of online topics. Modeling topic-dynamics: We consider the size of the communities in time as a proxy for online popularity dynamics. We find that the distributions of gains and losses, as well as the interevent times are fat-tailed indicating occasional, but large and sudden changes in the usage of hashtags. Inspired by typical website designs, we propose a stochastic model that incorporates a ranking with respect to a time-dependent prestige score. This causes occasional cascades of rank shift events and reproduces the observations with good agreement. This offers an explanation for the observed dynamics, based on characteristic elements of online media.
- ItemLocal asymptotics for the area of random walk excursions(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach, 2013) Denisov, Denis; Planat, Martin; Saniga, VitaliWe prove a local limit theorem for the area of the positive exursion of random walks with zero mean and finite variance. Our main result complements previous work of Caravenna and Chaumont, Sohier, as well as Kim and Pittel.
- ItemNon-trivial linear bounds for a random walk driven by a simple symmetric exclusion process(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Soares dos Santos, RenatoLinear bounds are obtained for the displacement of a random walk in a dynamic random environment given by a one-dimensional simple symmetric exclusion process in equilibrium. The proof uses an adaptation of multiscale renormalization methods of Kesten and Sidoravicius.
- ItemAging in the GREM-like trap model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Gayrard, Veronique; Gün, OnurThe GREM-like trap model is a continuous time Markov jump process on the leaves of a finite volume L-level tree whose transition rates depend on a trapping landscape built on the vertices of the whole tree. We prove that the natural two-time correlation function of the dynamics ages in the infinite volume limit and identify the limiting function. Moreover, we take the limit L→ ∞ of the two-time correlation function of the infinite volume L-level tree. The aging behavior of the dynamics is characterized by a collection of clock processes, one for each level of the tree. We show that for any L, the joint law of the clock processes converges. Furthermore, any such limit can be expressed through Neveu's continuous state branching process. Hence, the latter contains all the information needed to describe aging in the GREM-like trap model both for finite and infinite levels.
- ItemExtremal aging for trap models(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Gün, OnurIn the seminal work [5], Ben Arous and Cerný give a general characterization of aging for trap models in terms of α-stable subordinators with α ∈ (0,1). Some of the important examples that fall into this universality class are Random Hopping Time (RHT) dynamics of Random Energy Model (REM) and p-spin models observed on exponential time scales. In this paper, we explain a different aging mechanism in terms of extremal processes that can be seen as the extension of α-stable aging to the case α=0. We apply this mechanism to the RHT dynamics of the REM for a wide range of temperature and time scales. The other examples that exhibit extremal aging include the Sherrington Kirkpatrick (SK) model and p-spin models [6, 9], and biased random walk on critical Galton-Watson trees conditioned to survive [11].
- ItemAnnealed vs quenched critical points for a random walk pinning model(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2008) Birkner, Matthias; Sun, RongfengWe study a random walk pinning model, where conditioned on a simple random walk $Y$ on $Z^d$ acting as a random medium, the path measure of a second independent simple random walk $X$ up to time $t$ is Gibbs transformed with Hamiltonian $-L_t(X,Y)$, where $L_t(X,Y)$ is the collision local time between $X$ and $Y$ up to time $t$. This model arises naturally in various contexts, including the study of the parabolic Anderson model with moving catalysts, the parabolic Anderson model with Brownian noise, and the directed polymer model. It falls in the same framework as the pinning and copolymer models, and exhibits a localization-delocalization transition as the inverse temperature $beta$ varies. We show that in dimensions $d=1,2$, the annealed and quenched critical values of $beta$ are both 0, while in dimensions $dgeq 4$, the quenched critical value of $beta$ is strictly larger than the annealed critical value (which is positive). This implies the existence of certain intermediate regimes for the parabolic Anderson model with Brownian noise and the directed polymer model. For $dgeq 5$, the same result has recently been established by Birkner, Greven and den Hollander via a quenched large deviation principle. Our proof is based on a fractional moment method used recently by Derrida, Giacomin, Lacoin and Toninelli to establish the non-coincidence of annealed and quenched critical points for the pinning model in the disorder-relevant regime. The critical case $d=3$ remains open.
- ItemZero-one law for directional transience of one-dimensional random walks in dynamic random environments(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Orenshtein, Tal; Santos, Renato Soares dosWe prove the trichotomy between transience to the right, transience to the left and recurrence of one-dimensional nearest-neighbour random walks in dynamic random environments under fairly general assumptions, namely: stationarity under space-time translations, ergodicity under spatial translations, and a mild ellipticity condition. In particular, the result applies to general uniformly elliptic models and also to a large class of non-uniformly elliptic cases that are i.i.d. in space and Markovian in time.
- ItemRandom walk on random walks: Low densities(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2017) Blondel, Oriane; Hilário, Marcelo R.; Santos, Renato dos; Sidoravicius, Vladas; Teixeira, AugustoWe consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on particles. Surprisingly, the random walker may behave very differently depending on whether the underlying environment particles perform lazy or non-lazy random walks, which is related to a notion of permeability of the system. We also provide a strong law of large numbers, a functional central limit theorem and large deviation bounds under an ellipticity condition.