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We discuss uniform infinite causal triangulations and equivalence to the size biased branching process measure - the critical Galton-Watson branching process distribution conditioned on non-extinction. Using known results from the theory of…
We discuss weak coupling perturbation theory for lattice actions in which the fermions couple to smeared gauge links. The normally large integrals that appear in lattice perturbation theory are drastically reduced. Even without detailed…
We study simple nonequilibrium distributions describing a classical gas of particles interacting via a pair potential ${\phi}(x/{\epsilon})$, in the Boltzmann-Grad scaling ${\epsilon} \rightarrow 0$. We establish bounds for truncated…
Dissipative phase transitions are strongly shaped by the symmetries of the Liouvillian, yet the quantitative impact of weak and strong symmetries on critical behavior has remained unclear. We study a squeezed-photon model with single- and…
Fluctuating hydrodynamics is used to describe the total energy fluctuations of a freely evolving gas of inelastic hard spheres near the threshold of the clustering instability. They are shown to be governed by vorticity fluctuations only,…
We study the thick points of branching Brownian motion and branching random walk with a critical branching mechanism, focusing on the critical dimension $d = 4$. We determine the exponent governing the probability to hit a small ball with…
The pinning of flux lattices by weak impurity disorder is studied in the absence of free dislocations using both the gaussian variational method and, to $O(\epsilon=4-d)$, the functional renormalization group. We find universal logarithmic…
We analyze Mode Coupling discontinuous transition in the limit of vanishing discontinuity, approaching the so called "$A_3$" point. In these conditions structural relaxation and fluctuations appear to have universal form independent from…
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak convergence result for the fluctuation process and use it for…
We seek the possibility of a disorder driven transition in a tight-binding lattice with a flat band using complexity parameter approach. Our results indicate the existence of a localized to extended states transition with increasing…
An explicit expression is derived for the distribution function of end-to-end vectors and for the mean square end-to-end distance of a flexible chain with excluded-volume interactions. The Hamiltonian for a flexible chain with weak…
We analyze the Lattice Boltzmann method for the simulation of fluctuating hydrodynamics by Adhikari et al. [Europhys. Lett. 71, 473 (2005)] and find that it shows excellent agreement with theory even for small wavelengths as long as a…
Fluctuations of the amplitude of the order parameter govern the properties of superconducting systems close to the critical transition temperature. In the BCS regime we examine the contribution of these pairing fluctuations to the…
We study the quantum corrections to the Gross-Pitaevskii equation for two weakly linked Bose-Einstein condensates. The goals are: 1) to investigate dynamical regimes at the borderline between the classical and quantum behaviour of the…
We exhibit simple lattice systems, motivated by recently proposed cold atom experiments, whose continuum limits interpolate between real and $p$-adic smoothness as a spectral exponent is varied. A real spatial dimension emerges in the…
We study 2D nonlinear stochastic heat equations under a logarithmically attenuated white-noise limit with subcritical coupling. We show that solutions asymptotically exhibit Edwards-Wilkinson fluctuations. This extends work of Ran Tao,…
We establish explicit operator norm bounds and essential self-adjointness criteria for discrete Hodge Laplacians on weighted graphs and simplicial complexes. For unweighted $d$-regular graphs we prove the universal estimate…
We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear…
We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-$\epsilon$ Wilson-Fisher fixed point. Rather than…
We present a detailed study of the properties of the phase transition in the four-dimensional compact U(1) lattice gauge theory supplemented by a monopole term, for values of the monopole coupling $\lambda$ such that the transition is of…