相关论文: Exact Scaling Functions for Self-Avoiding Loops an…
We present approximate algorithms for performing smoothing in a class of high-dimensional state-space models via sequential Monte Carlo methods ("particle filters"). In high dimensions, a prohibitively large number of Monte Carlo samples…
The convergence of the derivative expansion of the exact renormalisation group is investigated via the computation of the beta function of massless scalar lambda phi^4 theory. The derivative expansion of the Polchinski flow equation…
We study the behavior of self avoiding polymers in a background of vertically aligned rods that are either frozen into random positions or free to move horizontally. We find that in both cases the polymer chains are highly elongated, with…
In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization.…
We study a proper-time renormalisation group, which is based on an operator cut-off regularisation of the one-loop effective action. The predictive power of this approach is constrained because the flow is not an exact one. We compare it to…
For directed polymers, the shape function computes the limiting average energy accrued by paths with a given average slope. We prove that, for a large family of directed polymer models in discrete time and continuous space in dimension…
We compute the exact vacuum expectation value of 1/2 BPS circular Wilson loops of ${\cal N}$=4 U(N) super Yang-Mills in arbitrary irreducible representations. By localization arguments, the computation reduces to evaluating certain…
The application of the exact renormalisation group to symmetric as well as asymmetric many-fermion systems with a short-range attractive force is studied. Assuming an ansatz for the effective action with effective bosons, describing pairing…
We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…
Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of…
Active polymers are driven out of equilibrium by internal forces and exhibit conformational properties that differ fundamentally from those of passive chains. Here we study how spatially modulated tangential activity reshapes the…
We illustrate the importance of mass scales and their relation in the specific case of the linear sigma model within the context of its one loop Ward identities. In the calculation it becomes apparent the delicate and essential connection…
High-dimensional limit theorems have been shown useful to derive tuning rules for finding the optimal scaling in random-walk Metropolis algorithms. The assumptions under which weak convergence results are proved are however restrictive: the…
A simple criterion to optimise coarse-grainings for exact renormalisation group equations is given. It is aimed at improving the convergence of approximate solutions of flow equations. The optimisation criterion is generic, as it refers…
We review recent results of the field theoretical renormalization group analysis on the scaling properties of star polymers. We give a brief account of how the numerical values of the exponents governing the scaling of star polymers were…
Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
We investigate the dissipation rate of a scalar field in the vicinity of the phase transition and the ordered phase, specifically within the universality class of model A. This dissipation rate holds significant physical relevance,…
We exploit the parquet formalism to derive exact flow equations for the two-particle-reducible four-point vertices, the self-energy, and typical response functions, circumventing the reliance on higher-point vertices. This includes a…
We consider height functions on symmetric spaces $M\cong G/K$ embedded in the associated matrix Lie group $G$. In particular we study the relationship between the critical sets of the height function on $G$ and its restriction to $M$. Also…