相关论文: Partition and generating function zeros in adsorbi…
We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of…
We study numerically, the distribution of the zeros of the grand partition function of $k$-mers on a $k \times L$ strip in the complex activity (z) plane. Using transfer matrix methods, we find that our results match the analytical…
We present a Weitz-type FPTAS for the ferromagnetic Ising model across the entire Lee--Yang zero-free region, without relying on the strong spatial mixing (SSM) property. Our algorithm is Weitz-type for two reasons. First, it expresses the…
Fractional kinetic equations employ non-integer calculus to model anomalous relaxation and diffusion in many systems. While this approach is well explored, it so far failed to describe an important class of transport in disordered systems.…
The partition function of a quantum field theory with an exact symmetry can be decomposed into a sum of functional integrals each giving the contribution from states with definite symmetry properties. The composition rules of the…
We consider a self-avoiding walk on the $d$-dimensional hypercubic lattice, terminally attached to an impenetrable hyperplane at which it can adsorb. When a force is applied the walk can be pulled off the surface and we consider the…
The hot nucleus $^{162}\mathrm{Dy}$ is investigated using covariant density functional theory, where the shell-model-like approach treats the pairing correlation. Lee-Yang's theorem is applied to classify the pairing phase transition by…
To analyze phase transitions in a nonequilibrium system we study its grand canonical partition function as a function of complex fugacity. Real and positive roots of the partition function mark phase transitions. This behavior, first found…
We use new algorithms, based on the finite lattice method of series expansion, to extend the enumeration of self-avoiding walks and polygons on the triangular lattice to length 40 and 60, respectively. For self-avoiding walks to length 40…
Beaton, Owczarek and Xu (2019) studied generating functions of Kreweras walks and of reverse Kreweras walks in the quarter plane, with interacting boundaries. They proved that for the reverse Kreweras step set, the generating function is…
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane. Using this approach, we are not only able to recover many…
We use anticommuting variables to study probability distributions of random variables, that are solutions of Langevin's equation. We show that the probability density always enjoys "worldpoint supersymmetry". The partition function,…
The density conjecture of Katz and Sarnak predicts that, for natural families of L-functions, the distribution of zeros lying near the real axis is governed by a group of symmetry. In the case of the universal family of automorphic forms of…
We consider a continuous-time simple symmetric random walk on the integer lattice $\mathbb{Z}^d$ in dimension $d \geq 3$, subject to a random potential given by a field of two-sided Wiener processes. In the high-temperature regime, we prove…
This is the second of two papers on the end-to-end distance of a weakly self-repelling walk on a four dimensional hierarchical lattice. It completes the proof that the expected value grows as a constant times \sqrt{T} log^{1/8}T (1+O((log…
Though classical random walks have been studied for many years, research concerning their quantum analogues, quantum random walks, has only come about recently. Numerous simulations of both types of walks have been run and analyzed, and are…
The dominant theme of this thesis is that random matrix valued analytic functions, generalizing both random matrices and random analytic functions, for many purposes can (and perhaps should) be effectively studied in that level of…
We study a system of N non-intersecting Brownian motions on a line segment [0,L] with periodic, absorbing and reflecting boundary conditions. We show that the normalized reunion probabilities of these Brownian motions in the three models…
We revisit the somewhat less studied problem of Yang-Lee zeros of the Ising antiferromagnet. For this purpose, we study two models, the nearest-neighbor model on a square lattice, and the more tractable mean-field model corresponding to…
The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N going to infinity they are strictly finite in number but their radius of gyration Rc is…