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  1. Mar 8, 2024We study a competition between two growth models with long-range correlations on the torus Tdn of size n in dimension d. We append the edge set of the torus Td n by including all non-nearest-neighbour edges, and from two source vertices, two first-passage percolation (FPP) processes start flowing on Td n and compete to cover the sites. The FPP processes we consider are long-range first-passage ...
  2. One of the consequences of our results is that for constant intensity competition, i.e. when the long-range parameters of the two processes are the same, while their rates differ by a constant multiplicative factor, coexistence of the two processes at the scale of the torus volume happen if and only if their global rates are equal.
  3. export.arxiv.org

    Mar 8, 2024One of the consequences of our results is that for constant intensity competition, i.e.\ when the long-range parameters of the two processes are the same, while their rates differ by a constant multiplicative factor, coexistence of the two processes at the scale of the torus volume happen if and only if their global rates are equal.
  4. ui.adsabs.harvard.edu

    One of the consequences of our results is that for constant intensity competition, i.e.\ when the long-range parameters of the two processes are the same, while their rates differ by a constant multiplicative factor, coexistence of the two processes at the scale of the torus volume happen if and only if their global rates are equal.
  5. semanticscholar.org

    One of the consequences of our results is that for constant intensity competition, i.e.\ when the long-range parameters of the two processes are the same, while their rates differ by a constant multiplicative factor, coexistence of the two processes at the scale of the torus volume happen if and only if their global rates are equal.
  6. semanticscholar.org

    We consider a model of long‐range first‐passage percolation on the d‐dimensional square lattice ℤd in which any two distinct vertices x,y ∊ ℤd are connected by an edge having exponentially… Expand 27 Highly Influential [PDF] 6 Excerpts
  7. paperswithcode.com

    Mar 8, 2024We study a competition between two growth models with long-range correlations on the torus T n d of size n in dimension d. We append the edge set of the torus T n d by including all non-nearest-neighbour edges, and from two source vertices, two first-passage percolation (FPP) processes start flowing on T n d and compete to cover the sites.
  8. link.springer.com

    Abstract We study a geometric version of first-passage percolation on the complete graph, known as long-range first-passage percolation. Here, the vertices of the complete graph Kn are embed-ded in the d-dimensional torus d Tn, and each edge e is assigned an independent transmission time Te e where is a rate-one exponential random variable associated with the Tdn Ee, Ee edge e, Tdn denotes the ...
  9. Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the model and measurements, and optimal (in the Bayesian sense) recursive formulations e.g. the Kalman Filter. However, they require significant domain knowledge to ...

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