arXiv subjects

Thomas Spencer

Publications and source records attributed to Thomas Spencer.

8 recordsLinked to original sources

arXiv2025

Deciphering the global production network from cross-border firm transactions

Critical for policy-making and business operations, the study of global supply chains has been severely hampered by a lack of detailed data. Here we harness international firm-level transaction data covering 20m global firms, and 1 billion cross-border transactions, to infer key inputs for over 1200 products. Transforming this data to a directed network, we find that products are clustered into three large groups including textiles, chemicals and food, and machinery and metals. European industrial nations and China dominate critical intermediate products such as metals, common components and tools, while industrial complexity is highly correlated with embeddedness in densely connected supply chains. Both forward and backward linkages are predictive of country-product diversification patterns, with stronger overall evidence for backward (upstream) linkages. Finally, we find structural similarities with AIPNET, a reference network generated via LLM queries, and strong linkages between products identified in manually-mapped electric vehicle battery and semiconductor supply chains.

econ.GN↗

arXiv2023

Continuous symmetry breaking along the Nishimori line

We prove continuous symmetry breaking in three dimensions for a special class of disordered models described by the Nishimori line. The spins take values in a group such as $\mathbb{S}^1$, $SU(n)$ or $SO(n)$. Our proof is based on a theorem about group synchronization proved by Abbe, Massoulié, Montanari, Sly and Srivastava [AMM+18]. It also relies on a gauge transformation acting jointly on the disorder and the spin configurations due to Nishimori [Nis81, GHLDB85]. The proof does not use reflection positivity. The correlation inequalities of [MMSP78] imply symmetry breaking for the classical $XY$ model without disorder.

math.PR↗

arXiv2020

Global well-posedness for the cubic nonlinear Schr{ö}dinger equation with initial lying in $L^{p}$-based Sobolev spaces

In this paper we continue our study [DSS20] of the nonlinear Schrödinger equation (NLS) with bounded initial data which do not vanish at infinity. Local well-posedness on $\mathbb{R}$ was proved for real analytic data. Here we prove global well-posedness for the 1D NLS with initial data lying in $L^{p}$ for any $2 < p < \infty$, provided the initial data is sufficiently smooth. We do not use the complete integrability of the cubic nonlinear Schr{ö}dinger equation.

math.AP↗

arXiv2020

The nonlinear Schrodinger equation on Z and R with bounded initial data: examples and conjectures

We study the nonlinear Schrödinger equation (NLS) with bounded initial data which does not vanish at infinity. Examples include periodic, quasi-periodic and random initial data. On the lattice we prove that solutions are polynomially bounded in time for any bounded data. In the continuum, local existence is proved for real analytic data by a Newton iteration scheme. Global existence for NLS with a regularized nonlinearity follows by analyzing a local energy norm.

math.AP↗

arXiv2014

Bounds on the Lyapunov exponent via crude estimates on the density of states

We study the Chirikov (standard) map at large coupling $λ\gg 1$, and prove that the Lyapounov exponent of the associated Schroedinger operator is of order $\log λ$ except for a set of energies of measure $\exp(-c λ^β)$ for some $1 < β< 2$. We also prove a similar (sharp) lower bound on the Lyapunov exponent (outside a small exceptional set of energies) for a large family of ergodic Schroedinger operators, the prime example being the $d$-dimensional skew shift.

math-ph↗

arXiv2013

A strong central limit theorem for a class of random surfaces

This paper is concerned with $d=2$ dimensional lattice field models with action $V(\naϕ(\cdot))$, where $V:\R^d\ra \R$ is a uniformly convex function. The fluctuations of the variable $ϕ(0)-ϕ(x)$ are studied for large $|x|$ via the generating function given by $g(x,μ) = \ln _{A}$. In two dimensions $g"(x,μ)=\pa^2g(x,μ)/\paμ^2$ is proportional to $\ln|x|$. The main result of this paper is a bound on $g"'(x,μ)=\pa^3 g(x,μ)/\pa μ^3$ which is uniform in $|x|$ for a class of convex $V$. The proof uses integration by parts following Helffer-Sjöstrand and Witten, and relies on estimates of singular integral operators on weighted Hilbert spaces.

math-ph↗

arXiv2011

Strong Convergence to the homogenized limit of elliptic equations with random coefficients

Consider a discrete uniformly elliptic divergence form equation on the $d$ dimensional lattice $\Z^d$ with random coefficients. It has previously been shown that if the random environment is translational invariant, then the averaged Green's function together with its first and second differences, are bounded by the corresponding quantities for the constant coefficient discrete elliptic equation. It has also been shown that if the random environment is ergodic, then solutions of the random equation converge under diffusive scaling to solutions of a homogenized elliptic PDE on $\R^d$. In this paper point-wise estimates are obtained on the difference between the averaged Green's function and the homogenized Green's function for certain random environments which are strongly mixing.

math.AP↗

arXiv1994

Inverting sets and the packing problem

Given a set $V$, a subset $S$, and a permutation $π$ of $V$, we say that $π$ permutes $S$ if $π(S) \cap S = \emptyset$. Given a collection $\cS = \{V; S_1,\ldots , S_m\}$, where $S_i \subseteq V ~~(i=1,\ldots ,m)$, we say that $\cS$ is invertible if there is a permutation $π$ of $V$ such that $π(S_i) \subseteq V-S_i$. In this paper, we present necessary and sufficient conditions for the invertibility of a collection and construct a polynomial algorithm which determines whether a given collection is invertible. For an arbitrary collection, we give a lower bound for the maximum number of sets that can be inverted. Finally, we consider the problem of constructing a collection of sets such that no sub-collection of size three is invertible. Our constructions of such collections come from solutions to the packing problem with unbounded block sizes. We prove several new lower and upper bounds for the packing problem and present a new explicit construction of packing.

math.CO↗