Symmetric exclusion as a model of non-elliptic dynamical random conductances

We consider a finite range symmetric exclusion process on the integer lattice in any dimension. We interpret it as a non-elliptic time-dependent random conductance model by setting conductances equal to one over the edges with end points occupied by particles of the exclusion process and to zero elsewhere. We prove a law of large number and a central limit theorem for the random walk driven by such a dynamical field of conductances by using the Kipnis-Varhadan martingale approximation. Unlike the tagged particle in the exclusion process, which is in some sense similar to this model, this random walk is diffusive even in the one-dimensional nearest-neighbor case.Comment: Preliminary version, any comments are welcome. 9 page

Random Forests and Networks Analysis

D. Wilson~\cite{[Wi]} in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph. This algorithm provides a powerful tool in analyzing structures on networks and along this line of thinking, in recent works~\cite{AG1,AG2,ACGM1,ACGM2} we focused on applications of spanning rooted forests on finite graphs. The resulting main conclusions are reviewed in this paper by collecting related theorems, algorithms, heuristics and numerical experiments. A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how to describe metastable dynamics in finite settings by means of Markov intertwining dualities 3) coarse graining schemes for networks and associated processes 4) wavelets-like pyramidal algorithms for graph signals.Comment: Survey pape

Continuity and Anomalous Fluctuations in Random Walks in Dynamic Random Environments: Numerics, Phase Diagrams and Conjectures

We perform simulations for one dimensional continuous-time random walks in two dynamic random environments with fast (independent spin-flips) and slow (simple symmetric exclusion) decay of space-time correlations, respectively. We focus on the asymptotic speeds and the scaling limits of such random walks. We observe different behaviors depending on the dynamics of the underlying random environment and the ratio between the jump rate of the random walk and the one of the environment. We compare our data with well known results for static random environment. We observe that the non-diffusive regime known so far only for the static case can occur in the dynamical setup too. Such anomalous fluctuations give rise to a new phase diagram. Further we discuss possible consequences for more general static and dynamic random environment

Legal Instruments How to Involve End User Or Public in the Public Procurement Contract Adaptation to Future Needs

For procurement items with a long life cycle, it is very important to be able to achieve the efficiency of the result not only at the moment of acceptance of the performance, but also during its entire life cycle. Because in such a changing and dynamic development of the world, as it is now, it is impossible today to accurately predict the needs of the future consumer, or society. Thus, to ensure efficiency, it is essential that the customer has the opportunity to impact the execution of the contract not only during the procurement planning phase, but also during the life cycle of the procurement item. It is even more important not only in the procurement planning phase, but also during its implementation to ensure compliance of the performance with the needs and interests of the existing end users, or society. In practice, various ways are used to influence or amend the direction of execution of a civil contract, depending on whether the traditional public procurement or the Public-Private partnership (hereinafter - PPP) procedure is applied. The purpose of the study is to reveal the practical and legal aspects of how the end user, or society, can be involved in decision-making related to changes or additional works necessary for the effectiveness of the contract, thus ensuring their compliance with real-time needs. Methods/Approach The methodology of the research includes a conceptual research using the critical literature review, analysis of normative, evaluation of the dominant consensus, synthesis of possible solutions to legal and practical shortcomings of end user involvement in public resources spending procedures. Results: Authors come to conclusion that the involvement of the public through NGOs is essential so that its interests are taken into account throughout the procurement subject during the life cycle and it would also be possible to introduce innovations based on the needs of the society throughout the contract execution period. Reasonable way how to involve the end user (society) as a participant during whole life cycle of public procurement contract for to be able to contract adaptation for future needs could be PPP based on QHC - where institutional partnership includes NGO as representative of society.Peer reviewe

Law of large numbers for a class of random walks in dynamic random environments

In this paper we consider a class of one-dimensional interacting particle systems in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied/vacant sites has a local drift to the right/left. We adapt a regeneration-time argument originally developed by Comets and Zeitouni [2] for static random environments to prove that, under a space-time mixing property for the dynamic random environment called conemixing, the random walk has an a.s. constant global speed. In addition, we show that if the dynamic random environment is exponentially mixing in space-time and the local drifts are small, then the global speed can be written as a power series in the size of the local drifts. From the first term in this series the sign of the global speed can be read off. The results can be easily extended to higher dimension

Large deviation principle for one-dimensional random walk in dynamic random environment : attractive spin-flips and simple symmetric exclusion

Consider a one-dimensional shift-invariant attractive spin-ip system in equilibrium, constituting a dynamic random environment, together with a nearest-neighbor random walk that on occupied sites has a local drift to the right but on vacant sites has a local drift to the left. In [2] we proved a law of large numbers for dynamic random environments satisfying a space-time mixing property called cone-mixing. If an attractive spin-ip system has a finite average coupling time at the origin for two copies starting from the all-occupied and the all-vacant configuration, respectively, then it is cone-mixing. In the present paper we prove a large deviation principle for the empirical speed of the random walk, both quenched and annealed, and exhibit some properties of the associated rate functions. Under an exponential space-time mixing condition for the spin-ip system, which is stronger than cone-mixing, the two rate functions have a unique zero, i.e., the slow-down phenomenon known to be possible in a static random environment does not survive in a fast mixing dynamic random environment. In contrast, we show that for the simple symmetric exclusion dynamics, which is not cone-mixing (and which is not a spin-ip system either), slow-down does occur

Random walks in dynamic random environments

Random walks in dynamic random environments are random walks evolving according to a random transition kernel, i.e., their transition probabilities depend on a stochastic process called dynamic random environment. In this thesis, we study asymptotic properties of such random walks on the integer lattice, in which the dynamic random environment is given by an interacting particle system.Stieltjes Institute for MathematicsUBL - phd migration 201