5 problems

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The Oslo model roughness exponent conjecture
Oslo roughness conjecture. The roughness exponent is
Conjectureopendepinning oslo-model roughnessarXiv posted 2 days ago
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The depinning roughness conjecture for one-dimensional driven strings
Depinning roughness conjecture. Based on numerical simulations, the exponent is
Conjectureopendepinning random-media roughnessarXiv posted 2 days ago
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The Narayan–Middleton conjecture on charge-density waves and Abelian sandpiles
Let CDWs pinned by disorder undergo a depinning transition, and let the Abelian sandpile model be the corresponding sandpile model. Narayan–Middleton conjecture. CDWs pinned by dis…
Conjectureopenabelian-sandpile-models depinning statistical-physicsarXiv posted 2 days ago
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The Fedorenko–Le Doussal–Wiese conjecture on charge-density-wave depinning and loop-erased random walks
Let charge-density waves (CDWs) be pinned by disorder, and let LERWs denote loop-erased random walks. Fedorenko–Le Doussal–Wiese conjecture. The field theory of the depinning trans…
Conjectureopendepinning field-theory loop-erased-random-walksarXiv posted 2 days ago
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All-orders vanishing of the depinning rate in the large-mass limit
Let $r$ denote the depinning rate, and let $s\ll 1$ be the parameter corresponding to the large-mass limit. The perturbative generalized Lyapunov exponent is expanded in powers of…
Conjectureopendepinning directed-polymers random-potentialsarXiv posted 2 days ago

5 problems

The Oslo model roughness exponent conjecture

The depinning roughness conjecture for one-dimensional driven strings

The Narayan–Middleton conjecture on charge-density waves and Abelian sandpiles

The Fedorenko–Le Doussal–Wiese conjecture on charge-density-wave depinning and loop-erased random walks

All-orders vanishing of the depinning rate in the large-mass limit