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We introduce General Lotto games with Scouts: a General Lotto game with asymmetric information. There are two players, Red and Blue, who both allocate resources to a field. However, scouting capabilities afford Blue to gain information, with some probability, on the number of Red's resources before allocating his own. We derive optimal strategies for this game in the case of a single field. In addition we provide upper and lower bounds of the value of the game in a multi-stage case with multiple battlefields. We devise several ways to characterise the influence of information versus strength. We conclude by drawing qualitative insights from these characterisations and the game values, and draw parallels with military practice.

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the `active part' of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier-Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples., Comment: This paper supersedes arXiv:1910.03350. 26 pages

We consider the Symmetric Exclusion Process on a compact Riemannian manifold, as introduced in van Ginkel and Redig (2020). There it was shown that the hydrodynamic limit satisfies the heat equation. In this paper we study the equilibrium fluctuations around this hydrodynamic limit. We define the fluctuation fields as functionals acting on smooth functions on the manifold and we show that they converge in distribution in the path space to a generalized Ornstein-Uhlenbeck process. This is done by proving tightness and by showing that the limiting fluctuations satisfy the corresponding martingale problem., Comment: 14 pages

We consider the symmetric exclusion process on suitable random grids that approximate a compact Riemannian manifold. We prove that a class of random walks on these random grids converge to Brownian motion on the manifold. We then consider the empirical density field of the symmetric exclusion process and prove that it converges to the solution of the heat equation on the manifold., Comment: 34 pages. Minor changes

In this article we aim at defining the discrete Gaussian free field (DGFF) on a compact manifold. Since there is no canonical grid approximation of a manifold, we construct a random graph that suitably replaces the square lattice $\mathbb{Z}^d$ in Euclidean space, and prove that the scaling limit of the DGFF is given by the manifold continuum Gaussian free field (GFF). Furthermore using Voronoi tessellations we can interpret the DGFF as element of a Sobolev space and show convergence to the GFF in law with respect to the strong Sobolev topology., Comment: 21 pages, minor changes, accepted for publication in Stochastic Processes and their Applications (available at https://www.sciencedirect.com/science/article/pii/S0304414919301310)

We prove that the "Immediate Exchange Model" of econophysics has a discrete dual, where the duality functions are those connecting the Brownian Energy Process and the Symmetric Inclusion Process. As a consequence, we recover invariance of products of Gamma distributions with shape parameter 2, and obtain ergodicity results. Next we show similar properties of a generalized model, where the exchange fraction is $Beta(s,t)$ distributed (instead of uniform), and product measures with $\mbox{Gamma}(s+t)$ marginals are invariant. We prove that the discrete dual has the self-duality property, and prove full SU(1,1) for both the continuous and discrete model., Comment: 24 pages, one figure. Substantial reworking on the previous version; proof of self-duality for the general case, full SU(1,1) of the continuous and discrete model