Open problems

1131 registered problems.

OP-00401 Solution claimed

Non-explosion of Brownian Fleming–Viot systems in arbitrary domains

PR · AIM Open Applied Problems · Fleming–Viot particle systems · killed Brownian motion

OP-00402 Solution claimed

Additivity of entanglement of purification

MP · additivity · AIM Open Applied Problems · entanglement of purification · von Neumann entropy

OP-00403 Solution claimed

Does supercritical percolation preserve transience?

PR · AIM Open Applied Problems · Cayley graphs · percolation · random walks

OP-00404 Solution claimed

The sharp matroid secretary conjecture

OC · AIM Open Applied Problems · matroids · online algorithms · secretary problems

OP-00405 Open

The density conjecture for activated random walk on the square lattice

PR · activated random walk · AIM Open Applied Problems · interacting particle systems · self-organized criticality

OP-00406 Open

The factor-two integrality gap for asymmetric metric routing

OC · AIM Open Applied Problems · integrality gaps · linear programming relaxations · traveling salesman problem

OP-00407 Open

Consensus in the one-dimensional Axelrod model above the feature threshold

PR · AIM Open Applied Problems · Axelrod model · clustering · interacting particle systems

OP-00408 Open

Poisson nearest-neighbor spacings on almost every flat torus

NT · AIM Open Applied Problems · binary quadratic forms · flat tori · level spacings

OP-00409 Open

The exact asymptotic match fraction for independent binary sequences

PR · AIM Open Applied Problems · longest common subsequences · random sequences

OP-00410 Open

Is the variance of fair binary sequence alignment linear?

PR · AIM Open Applied Problems · longest common subsequences · sequence alignment · variance bounds

OP-00411 Open

Does a bound bipolaron ever break rotational symmetry?

MP · AIM Open Applied Problems · polarons · symmetry breaking

OP-00412 Open

Bourgain–Spencer accuracy for random elliptic media at finite contrast

AP · AIM Open Applied Problems · higher-order homogenized equations · stochastic homogenization

OP-00413 Solution claimed

Selection of the carbon-monoxide poisoning phase

PR · absorbing states · AIM Open Applied Problems · catalytic surface reactions · interacting particle systems

OP-00414 Open

Competitive exclusion in a chemostat with unequal removal rates

DS · AIM Open Applied Problems · chemostats · competitive exclusion · Lyapunov functions

OP-00415 Open

Rapid sampling of proper colorings at the ergodicity threshold

PR · AIM Open Applied Problems · Glauber dynamics · mixing times · proper colorings

OP-00416 Open

Competitive exclusion with unequal death rates

PR · AIM Open Applied Problems · competitive exclusion · multitype contact process

OP-00417 Open

Subunit-moment eigenvalue bounds for complex Schrödinger potentials

SP · AIM Open Applied Problems · complex potentials · Lieb–Thirring inequalities · non-self-adjoint operators

OP-00418 Open

Weak survival of the contact process on nonamenable Cayley graphs

PR · AIM Open Applied Problems · Cayley graphs · contact process · nonamenable groups

OP-00419 Open

Polynomial equilibration at the four-state planar Potts critical point

PR · AIM Open Applied Problems · Glauber dynamics · mixing times · Potts model

OP-00420 Solution claimed

Global regularity for critical SQG with state-dependent noise

PR · AIM Open Applied Problems · global regularity · multiplicative noise · surface quasi-geostrophic equations

OP-00421 Solution claimed

Does subcritical heat flow always decay faster?

AP · AIM Open Applied Problems · criticality theory · heat kernels · Schrödinger operators

OP-00422 Open

Coexistence for every positive cyclic invasion rate

PR · AIM Open Applied Problems · coexistence · cyclic competition · interacting particle systems

OP-00423 Open

Constant-gap NP-hardness of densest k-subgraph

CO · AIM Open Applied Problems · densest k-subgraph · hardness of approximation

OP-00424 Solution claimed

A continuous strictly decreasing moment spectrum for Gaussian polymers

PR · AIM Open Applied Problems · directed polymers · disordered systems · martingales

OP-00425 Open

Classical attenuation versus uniform semiclassical local decay

AP · AIM Open Applied Problems · dissipative Schrödinger operators · local decay · semiclassical analysis

OP-00426 Open

A deterministic nontrivial growth exponent for planar DLA

PR · AIM Open Applied Problems · diffusion-limited aggregation · harmonic measure · random growth models

OP-00427 Open

Positive-temperature order in the three-dimensional Edwards–Anderson spin glass

PR · AIM Open Applied Problems · Edwards–Anderson model · replica overlaps · spin glasses

OP-00428 Open

Complete EFX allocation of indivisible goods with additive values

CO · AIM Open Applied Problems · envy-free allocations · fair division

OP-00429 Open

Does entanglement-assisted capacity equal the Lovász bound?

CO · AIM Open Applied Problems · entanglement-assisted communication · Lovász number · zero-error capacities

OP-00430 Open

Gaussian fluctuations of the optimal Euclidean traveling-salesman tour

PR · AIM Open Applied Problems · central limit theorems · geometric probability · traveling salesman problem

OP-00431 Open

Does exclusion equilibrate as fast as independent particles?

PR · AIM Open Applied Problems · exclusion processes · interacting particle systems · mixing times

OP-00432 Solution claimed

Accuracy of parsimony reconstruction under a molecular clock

PR · AIM Open Applied Problems · ancestral state reconstruction · maximum parsimony · phylogenetic trees

OP-00433 Open

The two-thirds passage-time variance exponent

PR · AIM Open Applied Problems · first-passage percolation · fluctuation exponents · KPZ universality

OP-00434 Open

Monotonicity of transport speed on Galton–Watson trees

PR · AIM Open Applied Problems · biased random walks · Galton–Watson trees

OP-00435 Open

Tracy–Widom fluctuations for a Gaussian lattice polymer at fixed temperature

PR · AIM Open Applied Problems · directed polymers · KPZ universality · Tracy–Widom distribution

OP-00436 Open

Balanced Gaussian simplex noise stability for four or more classes

PR · AIM Open Applied Problems · Gaussian partitions · noise stability

OP-00437 Open

A constant approximation for general max-min fair allocation

OC · AIM Open Applied Problems · approximation algorithms · max-min fair allocation

OP-00438 Open

The GNRS conjecture for minor-free network flow

CO · AIM Open Applied Problems · graph minors · metric embeddings · multicommodity flows

OP-00439 Open

A phase transition for continuum hard disks

PR · AIM Open Applied Problems · Gibbs point processes · hard disks · phase transitions

OP-00440 Open

A periodic high-density limit for bounded-confidence opinion clusters

PR · AIM Open Applied Problems · Hegselmann–Krause model · opinion dynamics · Poisson point processes

OP-00441 Open

Antiferromagnetic order in the half-filled square-lattice Hubbard model

MP · AIM Open Applied Problems · antiferromagnetism · Hubbard models · long-range order

OP-00442 Open

Global L2 scattering for the planar hyperbolic cubic Schrödinger equation

AP · AIM Open Applied Problems · dispersive equations · nonlinear Schrödinger equations · scattering

OP-00443 Open

A resonance gap for arbitrary uniformly hyperbolic trapping in three dimensions

SP · AIM Open Applied Problems · hyperbolic trapped sets · scattering resonances · semiclassical analysis

OP-00444 Open

Does stronger ferromagnetic coupling always slow Ising relaxation?

PR · AIM Open Applied Problems · Glauber dynamics · Ising model · spectral gaps

OP-00445 Open

Polynomial mixing of planar Ising dynamics with plus boundary

PR · AIM Open Applied Problems · Glauber dynamics · Ising model · mixing times

OP-00446 Open

A constant comparison between systematic and random Ising updates

PR · AIM Open Applied Problems · Glauber dynamics · Ising model · mixing times

OP-00447 Open

A roughening transition in the three-dimensional Ising model

PR · AIM Open Applied Problems · Gibbs measures · interfaces · Ising model

OP-00448 Open

The bosonic Laughlin contact-interaction gap

MP · AIM Open Applied Problems · Laughlin states · rotating Bose gases · spectral gaps

OP-00449 Open

Uniqueness of a boson star at every subcritical mass

AP · AIM Open Applied Problems · boson stars · ground states · pseudo-relativistic Hartree equations

OP-00450 Open

Liouville invariance under changing local moves on a Cayley network

PR · AIM Open Applied Problems · Liouville property · Poisson boundaries · random walks on groups